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Dominant patterns of interannual variability in the North Atlantic

St. John's

by

Farhana Nahed

A thesis submitted to the

School of Graduate Studies

in partial fulfillment of the

requirements for the degree of

Master of Science

Computational Science Program

Memorial University ofNewfoundland

August 2007

Newfoundland

Abstract

The low frequency variability of surface climate over the North Atlantic is described

using 55 years of observations from the Comprehensive Ocean-Atmospheric Data set and

NCEP reanalysis. Results are based on empirical orthogonal function analysis of sea

surface temperature (SST), air temperature, wind, heat flux, and precipitation. The

dominant spatial patterns of these parameters and sea level pressure are identified by

using canonical correlation analysis. It is shown that the zonal wind and air temperature

in the Labrador Sea are strongly correlated with the dominant modes of variability in the

atmospheric circulation. The SST anomalies in the Labrador Sea are weakly correlated to

the Sea Level Pressure (SLP) dominant modes of variability especially during the decadal

periods of warming in the 1950s and the 1990s. It is suggested that the long term

variability in the ocean circulation and sea ice at decadal time scale play a major role for

the SST in the Labrador Sea during these periods.

Acknowledgements

First I would like to thank my supervisor Dr. Entcho Demirov for his continuous

guidance and suggestions. He has been encouraging and always helpful. Without his

guidance and support this thesis would not have taken this final form.

I would also like to thank all the faculty and staff of Computational Science program and

Physics and Physical Oceanography Department for their assistance and support

throughout my program. I would also like to thank Chris Stevenson for being so helpful

with all of my computer problem.

Finally, I would like to thank Monowar and my friends, my Mom, Dad and others who

have contributed to my research and thesis.

11

Table of Contents

Abstract

Acknowledgements

Table of Contents

List of Figures

1 Introduction

1.1 Scales of variability of Climatic System: causes, scales and

i

ii

iii

v

implications..................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .... 1

1.2 Implication of Climate Changes.......................................................... 5

1.3 The North Atlantic Oscillation ........................................................................ 6

1.4 Relations between atmospheric and the North Atlantic ocean

Variability................................................................................... 14

1.5 Problem description ........................................................................ 16

2 Methods of Data Analysis

2.1 Statistical Methods of Description and Understanding of Atmospheric and Ocean

data........................................................................................ 18

2.2 Empirical Orthogonal Functions ....................................................... 22

2.3 Canonical Correlation Analysis (CCA) ............................................... 25

lll

2.3.1 Canonical Correlation Patterns .................................................. 26

2.4 Computation of the Covariance Matrix ................................................ 30

2.4.1 Eigenvalues and Eigenvectors of a Square Matrix........................... 31

2.4.2 Data Structure..................................................................... 33

2.4.3 Algorithm ofEOF Analysis..................................................... 33

2.4.4 EOF Analysis Algorithm with Matlab ......................................... 35

2.5 Computation CC patterns after a transformation to EOF

Coordinates ............................................................................... 36

3 Seasonal, Interannual and lnterdecadal Variability of Atmospheric

Characteristics and Sea Surface Temperature in the North Atlantic

3.1 Seasonal Variability ....................................................................... 41

3.2 Inter-Annual and Inter-Decadal Variability ........................................... 50

4 Empirical Orthogonal Function Analysis of SST and Atmospheric Data

4.1 Dominant modes of variability of the North Atlantic atmospheric circulation

and NAO from 1948 to 2005 ............................................................ 60

4.2 EOF analysis of near surface atmospheric parameters and SST .................... 65

5 Canonical Correlation Analysis

5.1 Correlation Patterns of Variability in the North Atlantic ........................... 81

5.2 Correlation Patterns of Variability in the Labrador Sea ............................. 90

6 Conclusion and Future Works ...................................................... . 1 02

Abbreviations ................................................................................... . 104

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 106

IV

List of Figures

1.1 Idealized, schematic spectrum of Atmospheric Temperature ....................... .4

1.2 Satellite image of sea ice .................................................................. 5

1.3 North Atlantic oscillation index ........................................................... 8

1.4 Positive and negative NAO ............................................................... 1 0

3 .1 Seasonal mean air temperature .......................................................... 4 2

3.2 Seasonal mean zonal wind .............................................................. .44

3.3 Seasonal mean sea surface temperature .............................................. .47

3.4 Seasonal mean Total Heat Flux ........................................................ .49

3.5 Inter-annual and inter-decadal Variability of Air Temperature ..................... 51

3.6 Inter-annual and inter-decadal Variability of wind ................................... 54

3.7 Inter-annual and inter-decadal Variability ofSST ................................... 56

3.8 Inter-annual and inter-decadal Variability of heat flux .............................. 58

4.1 Dominant EOFs of SLP and their time series ofNA ................................. 64

4.2 Dominant EOFs of air temperature and time series ofNA .......................... 66

4.3 Dominant EOFs of air SST and time series ofNA ................................... 68

4.4 EOF analysis of SST (Deser & Blackmon) ........................................... 70

4.5 Time series of winter sea ice (Deser & Blackmon) .................................... 71

4.6 Dominant EOFs of wind and time series ofNA ........................................ 72

v

4.7 Dominant EOFs of precipitation and time series ofNA ............................... 74

4.8 Dominant EOFs of heat flux and time series ofNA ................................ 75

4.9 Difference of average heat flux winter month ofNA SLP EOF .................. 77

4.10 Difference of average thlST' I M ofNA SLP EOF (Cayan) .................... 78

5.1 Canonical correlation of SST in the North Atlantic ................................ 85

5.2 Canonical correlation of air temperature in the North Atlantic .................. 86

5.3 Canonical correlation of zonal wind in the North Atlantic ........................ 87

5.4 Canonical correlation of turbulent heat flux in the North Atlantic ............... 88

5.5 Canonical correlation of precipitation rate in the North Atlantic ................ 89

5.6 Canonical correlation of SST in the Labrador Sea ................................ 94

5.7 Water Transport Index .................................................................. 95

5.8 Canonical correlation of air temperature in the in the Labrador Sea ............. 98

5.9 Canonical correlation of zonal wind in the in the Labrador Sea ................. 99

5.10 Canonical correlation of turbulent heat flux in the Labrador Sea .............. 1 00

5.11 Canonical correlation of precipitation rate in the Labrador Sea ................ 1 01

Vl

1. INTRODUCTION

1.1 Scales of variability of Climate System: Causes, Scales and

implications

The climate has varied significantly and continuously on time scales ranging from years

to glacial periods and to the age of the earth. The variability of climate can be expressed

in terms of two basic modes: the forced variations, which are the response of the climatic

system to changes in the external forcing and the free variations due to internal

instabilities and feedbacks, leading to nonlinear interactions among the vanous

components of the climatic system.

The changes in the purely external factors that affect the climatic system, but are not

influenced by the climatic variables themselves, constitute what may be called the

external causes of climatic changes, whereas those changes that are related to nonlinear

interactions among the various physical processes in the internal system are called

internal causes. The distinction between the two classes of causes is not always very

clear.

The external causes comprise variations in both astronomical and terrestrial forcing. The

astronomical factors would include changes (a) in the intensity of solar irradiance; (b) in

the orbital parameters ofthe earth (eccentricity ofthe orbit, axial precession and obliquity

ofthe ecliptic); and (c) in the rate of rotation ofthe earth.

Among the terrestrial forcing we must consider (a) variations in atmospheric composition

(mixing ratios of carbon dioxide and ozone, aerosol loading, etc.) due to volcanic

eruptions and human activity; (b) variations of the land surface due to land use

(deforestation, desertification, etc.); (c) long-term changes of tectonic factors such as

continental drift, mountain-building processes, polar wandering, etc. Some other possible

terrestrial and astronomical forcing mechanisms are changes in solar output, the collision

of the earth with interplanetary matter, changes in volcanic activity, and changes in the

geothermal flux.

The internal causes are associated with many positive and negative feedback mechanisms

and other strong interactions between the atmosphere, oceans, and cryosphere. These

processes can lead to instabilities or oscillations of the system, which can either operate

independently or introduce strong modifications on the external forcing. Let us show by

some examples what we mean by the difference between an externally forced variation

and an internally free change. The seasonal or diurnal variations of the climate are clearly

related to the external astronomical forcing. But there are day-to-day weather variations

that take place independently of any changes in external forcing. These irregular

fluctuations with time scales of several days to a week may be connected with the

passage of migratory atmospheric perturbations (highs and lows on the weather map) or

with the passage of a frontal system. They are to be considered free, because they result

from the internal baroclinic instability of the zonal current which depends only on the

critical value of the latitudinal gradient of the temperature.

Figure 1.1 shows an idealized variance spectrum of the atmospheric temperature during

its past history as evaluated by Mitchell (1976). The analysis of the spectrum shows

several spikes and broader peaks. The spikes are astronomically dictated, strictly periodic

components of climate variation, such as the diurnal and annual variations and their

harmonics, whereas the broad peaks represent variations that are, according to Mitchell

(1976), either quasiperiodic or aperiodic however, with a preferred time scale of

2

energization. Many of these broad peaks cannot be directly explained by the known

external forcings. They indicate the existence of a strong free variability within the

system.

The peak at three to seven days is associated with the synoptic disturbances mainly at

mid-latitudes. The slightly raised region of the spectrum at 100-400 years is associated

with the "little ice age" that began near the early 17th Century with rapid expansion of the

mountain glaciers in Europe. The peak near 2500 years is perhaps due to the cooling

observed after the "climatic optimum," about 5000 years ago, which predominated during

the great ancient civilizations. The next three peaks are perhaps related to deterministic

astronomical variations of the orbital parameters of the earth, which are supposed to be

responsible for the ice ages (Milankovitch, 1941 ): ( a) the eccentricity of the orbit of the

earth with a cycle of about 1 00 000 years, (b) the axial precession with a cycle of around

22000 years, and (c) the change in the obliquity of the ecliptic or the axial tilt with a

period of about 41000 years. Finally, the peaks near 45 and 350 million years may,

according to Mitchell ( 197 6), be related to glaciations due to orogenic and tectonic

effects and to continental drift.

For a linear system the externally forced variations would lead to a simple relationship of

cause and effect: if the forcing is an oscillatory process the response of the system would

have exactly the same frequency. As we have seen, this is however, not always the case,

since the internal climatic system is inherently unstable and never reaches the equilibrium

state.

Climate variability results from complex interactions of forced and free variations

because the climate system is a dissipative, highly nonlinear system with many sources of

3

instabilities. The interactive and often nonlinear nature of the instabilities and the

feedback mechanisms of the climate system make it very difficult to obtain a

straightforward interpretation of cause and effect.

104 I I I I I I I I I I I T T

T SPECliUM SURFACE

103 t:-c -... " ;. .i = •• § ...

I 0 w

~ "D

u c z 10 2 E"

... §. c

-o( .

~

iii: ... o( " a ... c > ~ ~ §. ... w "i . ~I . c > ~

~ ... i= I ~ ~ :: j 10 5l

j I ... . ;. :: w a c~ D 0 ...

1111: E "D .. I £! ~Q

.., ... c I ... ;. ...

:::;:; ... 0

~ .. "D : :! ·:

~ 1t:- l

0.1 -1010 109 108 107 106 105 104 10 3 102 10 0.1 10-2 10-3 10-4

PERIOD IN YEARS

Figl.l: Idealized, schematic spectrum of atmospheric temperature between 1 o-4 and

1010yr adapted from Mitchell (1976)

4

1.2 Implication of Climate Changes

During the rece.nt two~three decades the climate change became a critical issue for the

annospheric and geophysical sciences. An important aspect of global changes is multi

and quasi-decadal, inter-annual climate variability. The North Atlantic is the only place in

the No11hcm Hemisphere where the atmosphere communicates deep oceanic water

masses through convective over-turning (falley 1984). Today we know that wanner

temperatures have been causing more and more ice to melt during summer in the

Nonl>ern Hemisphere. This change is linked directly to global wam1ing. In 2005 and

2006. the extent of winter icc was about 6% smaller than the average amount over the

past26 years. The retreat is also s ignificantly Larger than the Jong-tenn de<:reru;c of L .5%

to 2% in winter ice cover observed per decade over the same time period.

Fig 1.2: Tlu's S(IJel/ite image shows sea ice extent on II September 2006. The pink line

shows tlte ttverage ice extenf for Sep1en1ber, cn•eraged between 1979 and 2000 (Image:

NSIIX)

5

If sea surface temperature (SST) variations in the North Atlantic at the climatic timescale

are predicted it may be possible to improve the forecast of the global climate system.

Climate variability on decadal and longer time scales is a subject of increasing interest of

relevance. El Nino is perhaps the best-known example of the impact that changing sea

surface temperature has on our climate. Every three to seven years, this warming of

surface ocean waters in the eastern tropical Pacific brings winter droughts and deadly

forest fires in Central America, Indonesia, Australia, and southeastern Africa, and lashing

rainstorms in Ecuador and Peru. El Nino affects thousands of people worldwide, and

billions of dollars in economic impact. But changing SST patterns have broader

implications than just the El Nino and La Nina cycle.

In the Northern Hemisphere especially over the middle and high latitude during cold

month, the most prominent and recurrent pattern of atmospheric variability is the North

Atlantic oscillation (NAO). NAO refers to a redistribution of atmospheric mass between

the arctic and the subtropical Atlantic. NAO produces large changes in the mean wind

speed and direction over the Atlantic, the heat and moisture transport between the

Atlantic and the neighboring continents, and the intensity and number of storms, their

paths, and their weather. NAO has direct affect on agricultural harvests, water

management, and energy supply and demand.

1.3 The North Atlantic Oscillation

The North Atlantic Oscillation (NAO) is a climatic phenomenon in the North Atlantic

Ocean of fluctuations in the difference of sea-level pressure between the Icelandic Low

and the Azores high. Through east-west rocking motions of the Icelandic Low and the

6

Azores high, it controls the strength and direction of westerly winds and storm tracks

across the North Atlantic. It is related to and highly correlated with the so called Arctic

Oscillation.

The NAO is the dominant mode of winter climate variability in the North Atlantic region

ranging from central North America to Europe and much into Northern Asia. It is a large

scale seesaw in atmospheric mass between the subtropical high and the polar low. The

corresponding index (Fig 1.3) varies from year to year, but also exhibits a tendency to

remain in one phase for intervals lasting several years.

The NAO has a strong implication on the track of storms and depressions across the

North Atlantic Ocean and into Europe. The storm track exhibits variations from winter to

winter in its strength and position, but a particularly recurrent variation is for the storm

track to be either strong with a north-eastward orientation taking depressions into NW

Europe or weaker with an east-west orientation taking depressions into Mediterranean

Europe. Since the Atlantic storms that travel into Europe control the rainfall, there is a

strong influence on European precipitation patterns.

The year-to-year variability in storm tracks is associated with a change in the mean

atmospheric circulation averaged over the winter season. This variability is usually seen

in the anomalous sea level pressure (SLP) patterns associated with high or low NAO

winters. When the Iceland Low pressure centre is deeper than usual, the Azores High is

stronger than usual, and vice versa. The change in the mean atmospheric circulation

drives patterns of warming and cooling over much of the northern hemisphere. For

example, when the NAO index is high, the SLP gradient between Iceland and the

Azores/Iberia is enhanced, driving stronger westerly and southwesterly flow that carries

7

wann maritime air over the cold winter Eurasian land mass, bringing anomalously wann

winter temperatures.

Westerly wind<;: blo\o\~ng across the Atlantic, bring moist air into Europe. In years when

westerlies are strong, summers are cool. winters are mild and rain is frequent. If

westerlies are suppress..'(), the temperature is more extreme in summer and winter leading

to heat waves, deep freezes and reduced rainfalL

The permanent low·pressure system over fceland (the Icelandic Low) and the permanent

high-pressure system over the Azores (the Azores High) control the direction and

strength of westerly winds into Europe. A large dHlCrencc in the pressure at the two

stations (a high index year, denoted NAO+) leads to

N011h Atlantic Oscillation (NAO) index, 1864--2001 (Hurrell) J

l

0

-t

-1

ro m w w oo w ~ ~ ~ ~ ro w w ~ oo Fig l.J: North Atllmtic Oscillation Index

increased westerlies and. consequently, cool summers and mild and wet v.~nters in

Central Europe and its Atlantic fa~ade. In contras~ if the index is low (NAO-), westerlies

are suppressed, these areas sutTer cold v.~nters and s torms track southerly toward the

Mediterranean Sea. This brings increased stonn activity and minfall to southern Europe

and North Africa.

3

Especially during the months of November to April, the NAO is responsible for much of

the variability of weather in the North Atlantic region, affecting wind speed and wind

direction changes, changes in temperature and moisture distribution and the intensity,

number and track of storms.

Although having a less direct influence than for Western Europe, the NAO is also

believed to have an impact on the weather over much of eastern North America. During

the winter, when the index is high (NAO+ ), the Icelandic low draws a stronger

southwesterly circulation over the eastern half of the North American continent which

prevents Arctic air from plunging southward. In combination with the El Nino, this effect

can produce significantly warmer winters over much of the United States and southern

Canada.

The sea level pressure averaged over the winter is easier to measure than the storms

themselves, so the variability of the NAO can be measured by the difference between the

mean winter SLP at Gibraltar and the mean winter SLP over Iceland. Some people use

Lisbon or the Azores instead of Gibraltar, but it makes little difference.

The Positive NAO index phase shows a stronger than usual subtropical high pressure

center and a deeper than normal Icelandic low. The increased pressure difference results

in more and stronger winter storms crossing the Atlantic Ocean on a more northerly

track. This results in warm and wet winters in Europe and in cold and dry winters in

northern Canada and Greenland. The eastern US experiences mild and wet winter

conditions

9

Fig 1.4:/..efl Panel Positive Nor1h Atlantic Oscillation Righi Panel Negative North

Atlamic Oscillation.

The negative NAO index pha.o;e shows a weak subtropical lllg)l and a weak Icelandic low.

The rcduc(..-d pressure gradient results in fewer and weaker winter storms crossing on a

more wcst·east pathway. They bring moist air into the Mediterranean and cold air to

northen1 Europe. The US cast coast experiences more cold air outbreaks and hence

snowy weather conditions. Greenland, however, will have milder winter temperatures.

The NAO and its time dependence for instance appear central to the global change

debate. Surface temperatures over the Northern Hemisphere are likely wamler now than

at any other time over the past millennium (Mann et al .. 1999; Jones ct al., 2001) and the

rote of warming has been specially high over the past 40 years (Folland ct al .. 200 I;

Hansen et al.. 2002). A substantial fraction of this most recent \\tanning is linked to the

behavior of the NAO (Hurrell. 1996), in particular a trend in its index from large

tO

amplitude anomalies of one phase in the 1960s to large amplitude anomalies of the

opposite phase since the early 1980s. This change in the atmospheric circulation of the

North Atlantic accounts for several other remarkable alterations in weather and climate

over the extratropical Northern Hemisphere as well, and it has added considerably to the

debate over our ability to detect and distinguish between natural anthropogenic climate

changes. While it has long been recognized that the North Atlantic Ocean varies

appreciably with the overlying atmosphere (Bjerknes, 1964), another reason invigorated

interest in the NAO is that the richly complex and differential responses of the surface

layer, intermediate and deep layers of the ocean to NAO forcing are becoming better

documented and under stood (Visbeck et al, 1998). The intensity of winter time

convective renewal of intermediate and deep waters in the Labrador Sea and Greenland­

Iceland-Norwegian Seas for instance, is not only characterized by large interannual

variability, but also by interdecadal variations that appear to be synchronized with

fluctuations in the NAO (Dickson et al., 1996). These changes in turn affect the strength

and character of the Atlantic thermohaline circulation and the horizontal flow of the

upper ocean, thereby altering the oceanic poleward heat transport and the distribution of

sea surface temperature.

On seasonal time scales, the upper North Atlantic Ocean varies primarily in response to

changes in the surface winds, air-sea heat exchanges and freshwater fluxes associated

with NAO variations (Cayan, 1992a,b). This does not mean, however, that the

extratropical interaction is only one-way. The dominant influence of the ocean on the

overlying atmosphere is to reduce the thermal damping of atmospheric variations, and

this influence becomes greater on longer time scales. The extent to which the influence of

11

the ocean extends beyond this local thermodynamic coupling to affect the evolution and

dynamical properties of the atmospheric flow is probably small, but the effect is non-zero

(Robinson, 2000; Kushnir et al., 2002).

New statistical analyses have revealed patterns in North Atlantic SSTs that precede

specific phases of the NAO by up to 9 months, a link that likely involves the remarkable

tendency of the extratropical ocean to preserve its thermal state throughout the year

(Kushnir et al., 2002.) On longer time scales, recent modeling evidence suggests that the

NAO responds to slow changes in global ocean temperatures, with changes in the

equatorial regions playing central role. (Hoerling et al., 2001). A second pathway that

offers hope for improved predictability of the NAO involves links through which changes

in stratospheric wind patterns might exert some downward control on surface climate

(Thompson et al, 2000). The NAO has a demonstrated influence on the physics,

hydrology, chemistry and biology of freshwater ecosystem across Northern Hemisphere

(NH) (Straile et al., 2003).

The spatial pattern related to NAO can be identified from the eigenvectors of the cross­

covariance matrix,computed from the time variations of the grid point values of SLP or

some other climate variable. The eigenvectors, each constrained to be specially and

temporally orthogonal to the others, are then scaled according to the amount of total data

variance they explain. This linear approach assumes preferred atmospheric circulation

states come in pairs, in which anomalies of opposite polarity have the same spatial

structure. The largest amplitude anomalies in SLP usually occur during the boreal winter

months; however, throughout the year the leading pattern of variability is characterized

by a surface pressure dipole, and thus may be viewed as the NAO,although the spatial

12

pattern is not stationary (Barnston and Livezey, 1987; Hurrell and van Loon, 1997; Portis

et al., 2001 ). Since the eigenvectors are, by definition, structured to explain maximum

variance, it is expected that the "centers of action" of the leading EOFs will coincide with

the regions of strongest variability.

Most studies of the NAO focus on the NH winter months, when the atmosphere is most

active dynamically perturbations grow to their largest amplitudes. As a result, the

influence of the NAO on surface temperature and precipitation as well as on ecosystems

is also greatest at this time of the year.

In conclusion the North Atlantic Oscillation has a large climatic influence on the North

Atlantic Ocean and surrounding land masses. It is a major controlling factor in basic

meteorological variables such as surface wind, temperature and precipitation which have

large socio-economic impacts on energy, agriculture, industry, traffic and human health

throughout the whole of Europe and eastern North America.

Early in this century, scientists aware of the NAO also became interested in its socio­

economic impacts (Meinardus, 1905). When more recently the NAO came into the focus

of scientific work again, a number of studies considered the influence of this large scale

variability pattern on local meteorological quantities such as seasonal mean precipitation,

temperature and wind velocity (e.g. Wallace and Gutzler, 1981; Deser and Blackmon,

1993; Hurrell, 1995; Rogers, 1990; Malberg and Bokens, 1997; Ulbrich and Christof,

1999).

13

1.4 Relations between atmospheric and the North Atlantic Ocean

variability

There has been an intensification of efforts toward describing and understanding climate

variability in the North Atlantic Ocean, in the past decade. A significant fraction of that

variability is associated with the NAO. While the NAO state may be characterized by an

index of that pressure difference (e.g., Hurrell 1995), the NAO is so strong mode that

alternative indices based on surface air temperature differences (van Loon and Rogers

1978), storms (Rogers 1997), sea ice (Deser et al. 2000), sea surface temperature (SST)

patterns (Deser and Blackmon 1993; Kushnir 1994; Sutton and Allen 1997), or SST

gradients (Czaja and Marshall 2001), when regressed on SLP, yield much the same

dipole SLP anomaly patterns.

When averaged for the winter months, the SLP-based index (Hurrell 1995) exhibits

interannual to decadal and interdecadal fluctuations. High and low states of the NAO

index reflect enhanced and diminished midlatitude westerlies, with related shifts in wind

patterns and intensities of air-sea exchanges of heat (Cayan 1992a,b ), freshwater (Hurrell

1996), and momentum (Visbeck et al. 1998). Since the general oceanic circulation,

including upper ocean gyres and thermohaline overturning, is wind and buoyancy forced,

there is little surprise in finding oceanic patterns in the observational record that are

coordinated with the low frequency components of atmospheric variability. Notable are

SST anomalies that develop directly as a time-integrated response to persistent NAO air­

sea heat flux anomalies (Bjerknes 1964; van Loon and Rogers 1978; Deser and

Blackmon 1993; Kushnir 1994). If the NAO SLP-SST -heat content fluctuations were the

only signals of coordinated atmosphere--{)cean variability, then that association would be

14

amenable to a null hypothesis explanation: that the ocean integrates atmospheric forcing

to redden the spectral response relative to the forcing spectrum (Hasselmann 1976;

Frankignoul and Hasselmann 1977). Battisti et al. ( 1995), for example, hindcast winter

SST for the North Atlantic using observed atmospheric circulation anomalies and an

ocean simulated as a field of one-dimensional mixed layers on the top a diffusive deep

ocean (no advection). The relative success of this and similar SST hindcasts for large

areas of the North Atlantic has given considerable weight to the idea of mixed layer

integration of surface heat flux as the leading mode of extratropical ocean-atmosphere

interactions.

The upper ocean's mean advective-diffusive heat balance involves a large annual surface

heat flux from the midlatitude ocean into the overlying atmosphere, supported by oceanic

heat transport convergence into the region. Thus SST anomalies are more than merely

one-dimensional mixed layer responses to local atmospheric forcing; they reflect

departures of the heat balance from the climatological annual mean and seasonal cycles.

These departures can lead to interannual persistence of winter SST anomalies through a

reemergence mechanism (Alexander and Deser 1995) whereby a winter mixed layer

anomaly is seasonally sequestered beneath a summer thermocline and then reappears in

the subsequent winter.

The observations indicate that this mechanism acts both locally (viewing as an Eulerian

field) and in a Lagrangian framework. Underlying the decadal evolution of the observed

oceanic heat content patterns are not only the thermal inertia of winter mixed layer

dynamics but also modulations of the ocean gyre circulation.

15

1.4 Problem Description

The objective of this thesis is to evaluate the impact of the variability of the atmospheric

circulation on the Labrador Sea. This evaluation is done through analysis of available

data from observations and atmospheric reanalysis. One major goal of this work is to

assess if the variability of atmospheric near surface parameters and SST of the Labrador

Sea is predictable by using information about the SLP only. The later provides

information about the major modes of atmospheric circulation and their change in time.

The thesis includes analysis of the relation between SLP modes and variability of the

Labrador Sea based on the traditional methods of Empirical Orthogonal Function (EOF)

and Canonical Correlation Analysis (Chapter2).

The interannual variability of the North Atlantic is discussed in Chapter 3. Chapter 4

presents results from EOF analysis of the studied prameters. The discussion in Chapter 4

defines the major characteristics and events of the North Atlantic variability during the

recent 50 years.

Chapter 5 discusses the connection between the variability of the atmospheric circulation

and the interannual change of the near surface atmospheric parameters and SST in the

Labrador Sea.

16

Chapter 2

2. Methods of Data Analysis

This chapter describes the methods used in the analysis of long term variability in the

North Atlantic SST and atmospheric characteristics. The approach is based on the use of

statistical methods for analysis of simultaneous multivariate data. The aim of the study is

to describe the dominant patterns of spatial variability about the long term mean. This can

be accomplished through use of Empirical Orthogonal Functions (EOF) and Canonical

Correlation Patterns (CCA) analysis.

2.1 Statistical Methods of Description and Understanding of

Atmospheric and Ocean Data

The climate is a complex dynamical system and its variability is influenced by a great

number of external factors. In climate studies only small portion of these factors can be

considered, while the rest are usually considered as background noise. Correspondingly

we consider every climate characteristics X as a sum of two components

X=Xd +X'

Here X d is a deterministic part of X which is the subject of our study. X' is non­

deterministic, stochastic component of X' which is not correlated to X d •

17

The statistical approach has certain drawbacks due to the fact that small variations in

ocean and atmospheric characteristics which usually are considered as noise some times

can have significant impact on the large-scale variability. Ocean vertical mixing, for

instance, which has spatial scales of centimeters or millimeters, may have significant

impact on the large scale circulation. This feedback between the large and small scales is

due to the nonlinear dynamics of the climate system. Nonlinear components of the

hydrodynamic equations include important advective terms. The thermodynamic part also

contains various nonlinear processes. The nonlinearities make the climate system

unpredictable beyond certain characteristic times. These characteristic time scales are

different for the climate subsystems such as the ocean, atmosphere, lithosphere and

cryosphere. The climate subsystems also can interact in a complex way influencing each

other on different time scales. The interactions often have the character of positive and

negative feedbacks. One important feedback, which is a main interest of this study is the

feedback between SST and atmospheric circulation. The surface momentum and

buoyancy fluxes drive the ocean circulation. The ocean currents transport heat and salt

polewards. This transport heats the poles and makes the ocean surface in the polar and

subpolar areas warmer. At the same time the ocean surface temperature influences back

the atmospheric circulation. The feedback between the atmosphere and ocean processes is

observed at different scales in variability of the characteristics of the two sub-systems at

different scales. One example is ElNino and Southern Oscillation (ENSO) which is

observed in the results simultaneous variability in ocean and atmospheric characteristics

in the tropical Pacific Ocean at interannual time scale.

18

Another example is the North Atlantic Oscillation (NAO) which dominates atmospheric

circulation variability over the North Atlantic at a decadal time scale. While there is

strong evidence that NAO dominates the variability of atmosphere over the North

Atlantic and therefore the atmospheric forcing of ocean circulations, the importance of

SST to the atmosphere is not widely accepted

In this study, we assume that the long term sea surface temperature and atmospheric

characteristics over the North Atlantic Ocean consist of two components, one which is

related to the interaction between atmosphere and ocean over the North Atlantic and

second, which is stochastic. The latter is due to error in observations or calculation of the

ocean and atmospheric parameters, or is related to processes not observable in the

available data. EOF and CCA techniques are used in this study to identify patterns of

simultaneous variability in the atmosphere and surface layer of the North Atlantic Ocean.

Let X 1 represents certain atmospheric or oceanic characteristics at some vertical level.

X 1 is a vector of dimension N=m*n which contains values of the 2-dimensional

characteristics with dimension n in latitude and m in longitude. The mean state

expectation of X 1 is ji = E(X). Statistical parameters have considerable complexity in

the climatological context. In particular, the computed mean is not entirely reliable as an

estimate of the climate system's true long term mean state. The computed mean usually

contain errors caused by taking observations over a limited observing period, at a discrete

times and a finite number of locations. It may also be affected by the presence of

instrumental, recording, and transmission errors. The climatological mean should be

understood also to be a moving target because today's climate is different from that

which prevailed thousands years ago.

19

The time mean of the characteristics X 1

is denoted by p . Then the variability of X 1 IS

described in terms of anomalies X' = X 1

- p . The anomalies at two different points

often have a tendency to vary jointly. This 'co-variability' may be quantitavely described

by the covariance matrix Lxx = E(x ;x ;T )where E is the expectation operator. In

statistics covariance indicates the strength and direction of a linear statistical relationship

between two random variables. When the linear relationship is stronger, then the

covariance also becomes higher. The time mean (u) and covariance matrix I only

describe statistical properties of important class of random processes. A random variable,

or a random process, is said to be stationary if all the statistical parameters are

independent of time. As a result, parameters such as the mean and variance, also do not

change over time or position. Most statistical techniques assume that the observed

process is stationary.

Most climate parameters that are sampled more frequently that one per year are not

stationary but cyclo-stationary, simply because of the seasonal forcing of the climate

system. Long-term averages of monthly mean sea-level pressure exhibit a marked annual

cycle. The mean annual cycle is computed as monthly mean(fi(m),m = 1, .... 12). The

anomalies remaining after subtracting the monthly mean are:

In the following, the studied atmospheric and ocean characteristics will be assumed that

they are cyclo stationary. Two methods are used in this study to identify the major modes

of interannual variability. First EOF analysis is used to identify the dominant pattern in

20

anomaly fields of atmospheric and ocean characteristics. The canonical correlation

analysis is then applied in a study of the interrelation between basic modes of variability.

2.2 Empirical Orthogonal Functions

Lets consider a stochastic characteristic X with mean fi . Assume that the anomalies X;

K

can be expanded in to a finite series x; = Lai,t~i with time dependent coefficient iii,/

and fixed patterns ~~ (Empirical Orthogonal Functions) and K = m * n . The variance of

the time coefficients iii,t usually decreases quickly with increasing index i, so that good

K'

approximations X; ~ L iii it are usually possible for K' << n * m. The patterns are i=l

chosen to be orthogonal so that optimal coefficients iii,t are obtained by simply projecting

the anomalies X; onto the patterns~~ . The coefficients iii are the EOFs coefficients.

The first step of the EOF analysis is to find one pattern e1, such that

E I = E cllx - (X 'e I )e 1112

) is minimized. Here the scalar product IS defined as

where * denotes complex conjugate, and the norm isllall =~(a, a). This first step finds

the projection of the random vector X onto one-dimensional subspace spanned by the

fixed vector e 1 • The variance of X which is contained in this subspace is:

21

El = E(llxll2

- 2(x ,e1) * x 1e1 + (x ,e1 ) * (x ,e1

))

=E(IIxll2 -(x,el)*(x,el))

= var(X)- var((x ,e1)) (1)

where the variance of the random vector X is defined to be the sum of variances of the

elements ofX and T denotes matrix or vector transpose. It can be shown that

Var((x ,e1) )= e11 Lxx e1 where I is the covariance matrix of X. The solution for the

first EOF vector e1, which minimizes £ 1 =. (IIX -(X,e1)e1

11

2

) under the constraint

[[e 1[[ = 1 can be found by using method of the Lagrange multipliers with the constrain

[[e 1[[ = 1. The minimization of equation (1) leads to:

(2)

where t denotes complex conjugate of transposed vector. This equation means that the

first EOF is the eigenvector e1 of the covariance matrix Lxx eigenvalue A..

To find the second EOF we have repeated the same procedure by minimizing

The result is that e2 is the eigen vector of Lxx that corresponds to its second largest

eigenvalue /L 2 • This second pattern is orthogonal to the first because the eigenvectors of

a Hermitian matrix I xx are orthogonal to one another.

22

We can continue in this way to define the following EOFs. The result of this process may

be formulated in the following way:

Let X be an m-dimentional random vector with mean jl and covariance matrix Lxx. Let

A1 ~ A2 ~ ••• ~Am be the eigen values of Lxx and let e1 , ••• ,em be the corresponding

eigenvectors of unit length. Since Lxx is the Hermitian, the eigenvalues are non-negative

and the eigenvectors are orthogonal.

(i) The k eigenvectors that correspond to A,, ... , Ak minimize

k

(ii) Ek= Var(X)- LA; i=l

m

(iii) Var(X) =LA; i=l

The EOF coefficients or principal components a;= (x ,e;) =X 1 e;• = e1r X are

uncorrelated and hence independent. The covariance of a; and a 1

satisfies the relation:

cov(ai'a1 ) = E( ((x- fi }ei )((x- fi }e' )*) -~TE{I(X- -xx- -)' \_. 1 -iT"- j 1 -iT- f Q =e ~ -f.l, -p, r =e L..,.e =Aje e =

Usually major part of the variance of X can be represented by the first few EOFs. If the

original variable has m components the approximation of X by a= (ap ... ,ak) with

k' << K. Using only limited number of EOFs leads to a significant reduction of amount

23

of analyzed data while retaining most of the variance. It is possible to clearly associate

the first EOF with a known physical process but this is much more difficult to do with the

second EOF because it is constrained to be orthogonal to the first EOF. Additional

analysis is needed in order to connect the computed EOFs with the underlying dynamics.

This analysis is usually based on the existing knowledge about the process and/or

applications of statistical methods like CCA.

The basic hypothesis of the EOF analysis is that studied characteristics X may be split

into two parts - deterministic X d and stochastic noise X ' . In the EO F analysis we need to

distinguish between the EOFs which correspond to Xd and toX'. The former are the

ones, which are going to be used in pattern analysis.

After computing the EOF analysis, one needs to select the number of dominant EOFs,

which spawn the space of X d • The most popular procedure to separate physically relevant

and noise related EOFs is based on so called Rule N The latter is based on the

assumption that the phase space (spanned by all EOFs) can be splitted into two subspaces

one which contains only noise, and second, which contains dynamic variability. It is

assumed that the dynamical sub-space is spanned by the EOFs with large and well

separated eigen values. Another approach is suggested by North et al., (1982) which is

based on estimation of typical errors for i; and eigenvectors ~;

The North's "Rule-of-Thumb' states that

24

If the sampling error of a particular eigenvalue ~A is comparable to or larger than the

spacing between A, and a neighboring eigenvalue, then the sampling error ~e of the

EOFwill be comparable to the size ofthe neighboring EOF.

2.3 Canonical Correlation Analysis (CCA)

Canonical Correlation Analysis is used to study the joint variability of random vectors

- - - I - I X andY. The objective of CCA is to find a pair of patterns I x and I r so that the

correlation between linear combinations X T] x 1 and Y r] r

1 is maximized. A second pair

-z -z -r-z - -z of patterns I x and I r is found so that X I x and Y T I r are the most strongly

- - - T- I correlated linear combinations of X andY that are not correlated with X I x and

-r- 1 Y I r , and so on.

25

2.3.1 Canonical Correlation Patterns

Let us consider a m x dimensional random vector X and a my dimensional random

vector Y. It is required to find a m x dimensional vector j x and a my dimensional

vector j Y such that the inner products flx = (X, j x) and flY = ( Y, j Y) have maximum

correlation. i.e.:

p = Cov(flx ,flY)

~Var(flx )Var(flY) - T - - -lx Cov(X,Y)Iy

(1)

where flx and flr are called canonical variates. If a pair of vectors lx and IY

- -maximizes the above equation then all vectors ax I x and a Y I Y do the same for any

nonzero ax and ay . Thus I x and I Y can be arbitrary normalized. We can choose the

patterns such that

where I xx and I YY are the covariance matrices of X andY. The above equation can

be rewritten as p- f-T " 7 - X ~XY}y ( 4) where I xr is the cross covariance

matrix Ixx = E((x- it X x-v- jly )). Similarly to the approach used in previous section

26

vectors fx and are found by max1m1zmg

(5)

where s and 1J are Lagrange multipliers that are used to account for constraints (2) and

(3). Setting the partial derivatives of E to zero, we get

(6)

(7)

and

8 E T - -- = '"" f + 21]'"" + = 0 a]y L....xx X L..,.yylY (8)

which is equivalent to

(9)

- -Then (9) is substituted into (7) to obtain a pair of eigen-equations for fx and fr

(10)

(11)

The eigenvectors of the two matrices are related to each other through a simple equation:

if fx is a solution of equation (1 0) then I~~ I :r fx is a solution of equation (11)

provided that their joint eigenvalue is nonzero. Finally equation (4) is maximized by

- -letting fx and fr be the solution of equations (1 0) and (11) that corresponds to the

27

largest eigenvalue A= 4r;1J. We have got the canonical random variables fJx =\X, 1x)

and flY = \ Y, 1Y) that are most strongly correlated, the natural next step is to find the

value ofp. Using equation (4), (6), (8) and (2), (3) in sequence we find:

P2

= 1~ Lxr1Y1~"L:r1x = 41Jr; 1/Lxx1x1~Lrr1Y =A

In this way we have found that the correlation is the square root of the eigenvalue that

- -corresponding to eigenvectors fx and /y .

To obtain m =min( m x, my) pairs of patterns ( 1;, 1;) and m corresponding pairs of

canonical variates the derivation detailed above can be repeated.

(12)

(13)

with correlation P; = Cov(fJ;x ,fJ;Y) =A, i-1,2, ... ,m.

The canonical variates and patterns are indexed in order of deceasing eigenvalue A;. Pairs

of canonical variates are uncorrelated (i * j).

Cov ( fJ/, fJ/ ) = Cov(/]1Y, PI) = Cov ( /3/, PI ) = 0

- -Assume X and Y are of the same dimension of m. Then the canonical variates

jjx =(f31x, ... ,f3:,)' and jJY =(fJt, ... ,fJ~)'can be viewed as the result of coordinate

transforms that have been applied to X and Y . The transformations relate jjx and jJY to

28

To find F X we need jjX = ((x, n ), ... ,(x,f;) y = f~ X where fx is the m X m matrix

-. with eigenvector f~ in its ith column. Thus

Cov(x,jjx )= Cav(X,f~X)= Cav(x, x)fx = Lxx fx

Substituting equation (14) for X, we get

The columns of F x and F v .F ~ and F ~ , are called the canonical correlation patterns.

The canonical variates /3;x and flr are called also canonical correlation coordinates

are normalized to unit variance, the canonical correlation patterns are expressed in the

units of the field they represent and they indicate the typical strength of the mode

represent by the patterns.

29

2.4 Computation of the Covariance Matrix

The correlation matrix [R] is introduced as a device for compactly representing the

mutual correlations among K variables. The computation begins with the ( n x K) matrix

[X] of data values whose correlations are to be computed. Each row of this matrix is a

vector, consisting of one observation each of K variables. The number of these rows is

the same as the sample size, n, since each of these row vectors is a sample point (in K

dimensions). Thus, [X] is essentially just an ordinary data table. An individual data

element xi,k is the ith observation of the kth variable.

Define the (n * n) matrix [1 ], whose elements are all equal to 1. The (n x K) matrix of

anomalies (in the geophysical sense of variables with their means subtracted), or centered

data [X'] is then

[X']= [X] _ _!_[l][X] n

(1)

The second term in Equation (1) is a (nx K)matrix containing the sample means. Its n

rows are all the same, and each consists of the K sample means in the same order as the

corresponding variables appear in each row of [X]. Multiplying [X'] by the transpose of

itself, and dividing by n - 1, yields an estimation S of the covariance matrix L xx

[Lxxl=-1 [x'Y[x']

n-1

The covariance matrix [Lxx] is a symmetric (K x K) matrix whose diagonal elements

are the sample variances of the K variables, and whose other elements are the co variances

30

among the K variables. For example, s1,1 is the sample variance of the first variable, and

s1,2 is the sample covariance between the first and the second variables. Because

variances are so often expressed in terms of covariance matrices, it is fairly common to

see the notation S1

,1

for the sample variance, which is equivalent to the more common and

familiar s,2 •

2.4.1 Eigenvalues and Eigenvectors of a Square Matrix

The formal definition of an eigenvalue of a matrix A is that it is any value A, which is a

root of the characteristic equation of the matrix,

det( A - A * J) = 0

A is an eigenvalue of A if and only if there is a nonzero vector x, known as an

eigenvector (or sometimes a "right" eigenvector), with the property that

A*x=A*x

Note that there must also be a "left" eigenvector y, with the property

y * A = A'* y = A* y

The characteristic equation has exactly N roots, so a matrix has N eigenvalues. An

important consideration is whether any eigenvalue is a repeated root, which determines

how hard the eigenvector computation will be.

If a matrix has the maximum possible number of linearly independent eigenvectors

(namely N, the order of the matrix), then the eigenvalues and eigenvectors can be used to

diagonalize the matrix. This only happens when the matrix is normal.

31

A nonzero vector x is an eigenvector of the square matrix A if

A*x=lt*x

for some scalar value It, called the associated eigenvalue.

Sometimes this eigenvector is more particularly described as a right eigenvector, so that

we may also consider left eigenvectors, that is, vectors y for which it is true that

y * A = A '* y = J.1 * y for some scalar J.1 •

For every eigenvalue of a matrix, there is at least one eigenvector. Every nonzero

multiple of this eigenvector is also an eigenvector. If, and only if, an eigenvalue is a

repeated root, then there may be more than one linearly independent eigenvector

associated with that eigenvalue. In particular, if an eigenvalue is repeated 3 times, then

there will be 1, 2 or 3 linearly independent eigenvectors corresponding to that eigenvalue.

For many statistical applications, eigenvalues and eigenvectors are calculated for real (not

containing complex or imaginary numbers), symmetric matrices. Eigenvalues and

eigenvectors of such matrices have a number of important and remarkable properties,

some of which also hold for the eigenvalues and eigenvectors of square matrices more

generally. The first of these properties is that the eigenvectors of symmetric matrices are

orthogonal. That is, their dot products with each other are zero. Furthermore, since each

eigenvector is defined to have unit length, the dot product of any eigenvector with itself is

one:

T {l,i = j X X =

I J O,i ::j:. j

32

2.4.2 Data Structure

Let us assume that we have measurements of some variable at locations

(ApqJ1),(A2 ,qJ2 ) ••• (Ap,<f'p) taken at times fpt 2 , •• .tn where AK is latitude and <f'K is

longitude of kth points. For each times t 1 (j = 1, ... n) we can think of the p -dimensional

vector F1; (i = l, ... p) as one map of the field .We store this measurements in a matrix F as

n maps each being p points long. So one row of matrix F is one map for time t 1

• We

arrange each map into row vector in F with size p. We can then interpret each of the p

columns in F as a time series for a given location. The EOF analysis is performed using F

as the data matrix.

2.4.3 Algorithm of EOF Analysis

Let us assume that we have removed the mean from each of the p time series in F, so

that each column has zero mean. We form the covariance matrix ofF by calculating

R=FTF, and then we solve the eigenvalue problem. RC = CA

A is a diagonal matrix containing the eigenvalues A; of R . The c; column vector of C

are the eigenvectors of R corresponding to eigenvalues A; . Both A and C are the size

p x p. For each eigenvalue A; chosen we find the corresponding eigenvector C;. Each of

this eigenvectors can be regarded as a map. These eigenvectors are the EOFs we are

looking for. In what follows we always assume that the eigenvectors are ordered

according to the size of the eigenvalues. Thus, EOFI is the eigenvector associated with

33

the biggest eigenvalue, and the one associated with the second biggest eigenvalue is

EOF2, etc. Each eigenvalue A; , gives a measure of the fraction of the total variance in R

explained by the mode. The value in percentage is found by dividing the A; by the sum

of all the other eigenvalues (the trace of A).

The eigenvector matrix C has the property that CTC=CCT=I or the EOFs are

uncorrelated over space. Another way of stating this is to say that the eigenvectors are

orthogonal to each other.

The pattern obtained when an EOF is plotted as a map, represents a standing oscillation.

The time evolution of an EOF shows how this pattern oscillates in time. To see how the

first EOF evolves in time we calculate:

The n components of the vector a1 are the projections of the maps in F on EOFl, and

the vector is a time series for the evolution ofEOFl. In general, for each calculated

EOFj, we can find a corresponding a1

. These are the expansion coefficients ofthe EOFs.

Just as the EOFs where uncorrelated in space, the expansion coefficients are uncorrelated

in time.

A common use of EOF is to reconstruct a cleaner version of the data by truncating this

sum at some j = N << p; that is, we only use the EOFs of the first (largest) few

eigenvalues or the most significant EOFs. The rational is that the first N eigenvectors

are capturing the dynamical behavior of the system and the other eigenvectors

(corresponding to the smallest eigenvalues) are just due to random noise. This

assumption does not always have to be true.

The algorithm for finding EOF is:

34

• First form matrix . from the observations, and remove the time mean of each

time series.

•

•

•

Then find the covariance matrix R=FTF .

Then find the eigenvalues and eigenvectors of R by solving RC = CA

Afterwards find the biggest eigenvalues and their corresponding eigenvectors, the

EOFs.

• Then find the expansion coefficients by calculating aj=FCj

2.4.4 EOF analysis Algorithm with Matlab

Matlab algorithm was developed for EOF analysis that includes the following steps.

• Define a matrix M, with each row as one map, and each column a time series for a

given station. That means in matrix M, the data need to be put in such a way that

row represents map and column represents time series.

• Remove the mean of the column.

• Form the covariance matrix by the command: R=F'*F;

• Calculate the eigenvalues and eigenvectors of the covariance matrix.

• Find the expansion coefficients corresponding to eigenvalue number i.

• Compute the vector giving the amount of variance explained for each eigenvalue.

35

2.5 Computation of CC patterns after a Transformation to EOF

Coordinates

In the calculation of CCA, if the data are transformed into EOF space before the analysis

the CCA algebra becomes considerably simpler. Suppose that only the first k x and

kr EOFs are retained, so that

(20)

We have used the renormalized versiOns of the EOFs and their coefficients

d -iT ( ~ )I I 2 - i an e = /l,; e . The CCA IS then applied to the random

- T - T vector X' = ( a1x +, •.. , a{,+) and Y' = (a{+, ... , a[y+) . An advantage of this approach is that

it is often possible to use only the first few EOFs.

Another advantage is that the algebra of the problem is simplified since Lxx· and

Ln" are both identity matrices. Thus according to the equations (10, 11) f~.and f~. are

T T eigenvectors of Lxr· Lxr· and Lxr· Lxr· respectively. As these are non-negative

definite symmetric matrices, the eigenvectors are orthogonal. Moreover, the canonical

correlation patterns F ~· = i ~· and F ~· = i ~· .

A minor disadvantage is that the patterns are given in the coordinates of the renormalized

EOF space. To express the pattern in the original coordinate space it is necessary to

reverse transformation (20) with (18) and (19):

36

The canonical correlation patterns are no longer orthogonal after the above back

transformation and f i- F.

37

Chapter 3

Seasonal, Interannual and Interdecadal Variability of Atmospheric Characteristics and Sea Surface Temperature in

the North Atlantic

The physical processes in the ocean surface layer play an important role in formation of

the atmosphere and ocean variability. The incident solar radiation absorbed by the ocean

heats the surface layer. The ocean surface is in contact with the atmosphere and

exchanges heat and water with the near surface air masses.

Seasonal and latitudinal variations in ocean sea surface temperature are driven primarily

by variations of insolation. The amount of solar radiation incident on the ocean surface

depends on the latitude, season and time of the day. The mean solar flux per unit area

perpendicular to the solar beam at the mean position ofEarth is equal to S0 = 1367 w/m2.

The Earth is approximately spherical; and the planets surface is heated differentially. The

solar heat flux at the ocean surface depends on the local solar zenith angle ()8 at each

latitude. It is equal to zero at the equator and approaches 90° at high latitudes. Beyond the

astronomical factors, the solar radiation incident to the ocean surface depends also on

atmospheric characteristics. The solar heat enters the atmosphere is partly reflected back

to the space and partly absorbed by the air molecules. The amount and spectrum of the

solar radiation at the ocean surface depends therefore on the content of greenhouse gasses

and clouds in the atmosphere.

38

The solar heat flux per unit area in the upper atmosphere is

where d is the mean distance from which the flux density S0 is measured, and d is the

actual distance from the sun. The solar radiation Q0 incident on the ocean surface is large

in the equatorial areas and smaller in the polar ocean. The ocean reflects back part of the

solar heat Q0 incident to its surface. The amount of the reflected radiation depends on the

roughness of the ocean surface. The strongest reflection is observed in the ocean areas

covered by ice. The part of the radiation reflected by the ocean surface is called albedo

as , which for the major part of the ocean has a value a 8 ~ 0.3. In the polar ocean as

may have values higher than 0.3.

The ocean emits back to the atmosphere outgoing long wave radiation R,, . It is greatest

over the tropical ocean, where cloud cover is relatively low. R,, is lowest in the polar

regions and in regions of persistent high cloudiness in the equatorial areas.

The zonal averaged annual mean net radiation

Rnet = Qo(l-a,)- RL

is positive equator-ward of 40° of latitude and negative pole-ward of that latitude.

Assuming that the ocean and atmosphere are in steady state conditions, which means that

long term annual mean ocean and atmospheric characteristics do not change, one can

write the balance of the energy at the ocean surface as

Rnet -LE-SH -Mea =0

39

where LE is the latent heat, SH the sensible heat, /!:,.Feo is the horizontal flux out of the

column of ocean below the ocean surface. We will often refer to !!:.Feo also as the

meridional heat flux. Mea is due to the horizontal circulation and turbulent mixing in

the ocean.

The meridional heat transport exists in both atmosphere and ocean. If this transport would

not exist, the tropics would be much warmer and the poles much colder. The net turbulent

heat flux.

HT =LE+SH

is the heat exchange through the ocean surface due to processes of turbulent mixing in the

boundary layers of atmosphere and upper ocean.

The near surface atmospheric and ocean characteristic depend in a complex way on the

surface energy balance. At the same time some of them like SST, atmospheric

temperature, humidity, wind speed influence the intensity of the heat exchange through

the surface. In this way, the near surface atmospheric and ocean characteristics may be

considered as important indicators for the long-term changes in state of the atmosphere

and ocean. This section presents analysis of interannual variability in the near surface

atmospheric characteristics and SST.

Following the previous studies ofKushnir (1994), Deser and Blackmon (1993) the winter

SST and atmospheric parameters are studied here. During the winter the convective

processes intensify the vertical turbulent mixing in the surface ocean layer. The depth to

which the vertical transport of heat reaches during this season varies usually from about

lOOm in mid-latitudes up to about 2000m in the deep convection areas. During the rest of

the year the vertical mixing is limited to a relatively thin surface layer.

40

In this chapter first the seasonal mean characteristics of SST, atmospheric temperature,

zonal wind and net turbulent heat flux are described. The seasonal variability usually is

much stronger than variability at interannual and interdecadal time scales. The later

however is important because it shows the tendencies in the ocean and atmospheric

variability at long time scales. The winter anomalies of SST and near surface atmospheric

characteristics are discussed in section 2.

3.1 Seasonal Variability

This section describes the seasonal variability of atmospheric characteristics and SST.

The seasonal mean parameters are calculated for winter December, January, February

(DJF), spring March, April, May (MAM), summer June, July, August (JJA) and autumn

September, October, November (SON) seasons. As described in the previous section the

near surface atmospheric characteristics and SST distribution depends on the radiative

fluxes, interaction between the atmosphere an ocean and atmospheric dynamics (see Fig

3.1 ). The dependence of the absorbed solar radiation on the latitude results in quasi-zonal

structure of atmospheric parameters i.e. their variability in zonal direction is smaller than

in meridional. The air temperature equatorward of 30lN, where the net radiative balance

is positive, is relatively high and remains between 20° and 30° during the whole year. In

the subpolar areas the seasonal mean air temperatures change from -5 to+ 10 degrees C.

41

a) Wonlef b) Spri!lll

c) Summer d) Aulllmn

0 • 10 " •

Fig 3.1 :Seasonal Mean Air Temperature (0C).(a)Winter,(b)Spring,(c)Summer.(d)Autumn

42

There is also a longitudinal change in the atmospheric temperatures during all seasons. In

all seasons the maximum of air temperature is in the western part of the tropical ocean.

This is the area of Gulf Stream, which transports warm waters along the North America

Coast. The Gulf Stream heat transport is a major contributor to the meridional ocean heat

transport in the subtropical North Atlantic. The atmospheric temperature in eastern

subtropical North Atlantic is colder than in western and central part of the basin. This is

an area of intensive upwelling, where cold waters are transported from the deep ocean to

the surface. The relatively cold ocean waters in the upwelling areas near the eastern coast

of the Sub-tropical North Atlantic cool the near surfaces air.

The atmospheric temperature differs also in the eastern and western part of the sub-polar

North Atlantic. As in the sub-tropics, this difference is due to the transport in the ocean.

The ocean current along the western coasts of the sub-polar North Atlantic transport cold

waters from the polar areas towards the Labrador Sea. This currents transport also sea-ice

which melts in spring in the Labrador Sea. The melting of the ice causes additional

cooling and freshening of the surface waters. The temperature in the eastern sub-polar

North Atlantic is influenced by the Gulf Stream, which transports warm waters, towards

the polar areas. The seasonal atmospheric temperatures here are 1 0° to 15° higher than in

the western part of the sub-polar North Atlantic.

The atmospheric zonal wind (Fig 3.2) over the North Atlantic is influenced by two major

elements of the atmospheric circulation. These are the passats in the tropical area

43

Fl'g 3.2: Seasonal Mean Zonal Wind (m/s). a) Winter b) Spring c) Summer d) Autumn

••

and westerlies in the mid-latitudes. The passat winds in the tropical area are

predominantly easterlies. They persist with some seasonal variability during the whole

year. The later is driven by the upward atmospheric flow in equatorial area. Here humid

air masses warmed by the ocean surface move upward. At high altitudes the dominant

flow is poleward, where the uplifted at the equator air masses, propagate towards the

tropics. The passats form the lower branch of Hadley circulation, and they bring dry air

masses towards the equator. Passats have a strong westward component, which is present

at low latitudes during all seasons (Fig 3.2 a, b, c, d). In summer the Hadley cell

intensifies in the Northern Hemisphere. Correspondingly the passats have their strongest

seasonal mean zonal component during this season (Fig 3.2c).

The westerlies in the mid and sub-polar latitudes persist during all seasons. This is the

area of polar jet stream. It forms between latitudes 30~ and 70~. The strong eastward

flow at high altitudes is formed due to the meridional gradient of atmospheric

temperature and is a consequence of the thermal wind relation, which governs the large­

scale geophysical flows. Additionally there is a tendency of developing cyclonic

disturbances in mid-latitudes along the jet stream to form fronts. The frontogenesis

processes related to the dynamics of cyclones, result in concentration of north-south

temperature gradients into relatively narrow regions. This contributes to the sharpness of

the jets. The area of positive zonal wind in mid-latitudes (Fig 3.2) is the zone where

intensive cyclones and related frontal systems pass the North Atlantic. During the winter,

the cyclones bring relatively cold and dry air masses over the North Atlantic.

Additionally the cyclonic atmospheric eddies are related with strong near surface winds.

As discussed in the beginning of this chapter, under these conditions the surface heat and

45

water fluxes intensify the areas where the contrast between atmospheric and ocean

temperature is high. The process of cyclogenesis is stronger in winter and autumn.

Correspondingly these are the seasons of strongest westerlies and related storms passing

the mid latitudes of North Atlantic. Strong easterlies are present along the eastern coast of

Greenland. They have strongest magnitude in winter and autumn.

The SST, as the atmospheric temperature has a well defined zonal distribution. The

equatorial and tropical areas of the North Atlantic are warm during the whole year. The

temperature here varies between 20° to 25°C with maximum in summer when the

absorbed solar radiation is higher. The minimum of the SST during all seasons is in the

sub-polar areas. Deviation from the zonal structure of SST distribution is observed in the

areas of western boundary currents- Gulf Stream, the Labrador Current and East

Greenland Current.

The Gulf Stream and its extension, the North Atlantic current, transports warm waters

towards the Northeastern part of the North Atlantic. The SST along the North American

coast and the western coast of Europe is high due to this transport. The Labrador Current

and the eastern Greenland current transport cold waters toward the coast of North East

North Atlantic. This flow, which during the winter and spring transports also sea-ice, has

the strongest impact on the SST during these seasons. Another area of deviation from the

zonal distribution of SST is in the North Western Africa upwelling region.

46

o 2 4 s a 10 12 14 18 18 ~ n

Fig 3.3: Seasonal 1\lean SST(°C). a) JY;nter. b) Spr;ng. c) Summer. d) Alllunm

47

The spatial and temporal variability of TA and SST have similar patterns. One reason for

this is the surface turbulent heat transport. The direction of the surface turbulent heat

transport across the surface is always towards the cooler component of the system ocean

atmosphere, which keeps TA and SST close.

Net heat flux Qnet consists of two radiative flux components, which are the surface

shortwave and longwave radiation and two components of the turbulent heat: sensible

and latent heat fluxes. Qnet over the oceans is one of the key parameters governing the

atmosphere-ocean interaction. It is required for weather prediction and climate studies

related to the global energy balance and water cycle. Using suitable models, net heat flux

can be used to reproduce and predict variations of the global ocean regime and its impact

on atmospheric dynamics, as well as variations in regional hydrological processes and

water resources and responses to such environmental changes as the increase in

greenhouse gas forcing. Here we discuss the seasonal variability of turbulent net heat flux

Hr . Its dominant component is the evaporative heat loss. The sensible heat exchange at

the ocean surface is smaller, except over the warm Gulf Stream.

H 7 is predominantly negative in the whole North Atlantic. In the tropics there is an area

of strong heat loss by the ocean, which coincides, with the zonal belt of passats winds.

This is the area of strong evaporation and negative latent heat flux. The turbulent heat

flux in the Gulf Stream area is negative during all the seasons. The heat loss by the ocean

here is strongest in winter when the contrast between the atmospheric and sea

temperatures is relatively large. Hr has high seasonal variability also in the Labrador and

Greenland seas.

48

Willet Sprilg

.... .,.. .. ., 0 "

Summer Autumn

Fig 3.4: Seosonol Meon Toto/ Heot Flux (JY!m1) (a) Winter, (b)Spring, (c) Summer, (d)

Armmm

49

These are two areas of deep water formation, which are strongly cooled during the winter

(Fig 3.4 a,b ). In summer the heat loss through the turbulent exchange here is relatively

weak.

3.2 Inter-Annual and Inter-Decadal Variability

In this section winter anomalies of atmospheric characteristics and SST are discussed.

The anomalies are calculated for winter months only and then averaged for every year.

The annual mean anomalies are then used to describe the interannual variability of the

North Atlantic.

As mentioned in the previous section the SST and near surface atmospheric temperature

are quasi-zonaly distributed. This fact was used in previous studies (see Kushnir,1994) of

the North Atlantic interannual variability, where the anomalies were studied separately in

several zonal belts of the basin. In the previous section it was shown that there are two

major areas in the North Atlantic which have different characteristics and dynamics: 1)

the subtropical North Atlantic is characterized by high SST, TA and wind (passats) which

have westward direction 2) the mid and high latitudes with colder atmosphere, ocean

surface and winds with predominant eastward direction. Here we study SST and

atmospheric characteristics averaged for these two regions.

50

a) PO!i>l11160 -11160

c) Period 1996 - 2005 .. OA

0

~· ...

b) Period 1970- 1960

.. 0

~· _,

-u

""'f,...L,--,ce,..c--::1001',--,ce,,.::--::1910=--,ce,.::---:-.,..~-,,.i

Fig 3.5: Inter-Annual and lntcr-Dccadal Variability of Air Temperature

51

Fig 3.5.d shows the air temperature anomaly averaged within two zonal belts,

20° ~ rp ~ 45° and 45° ~ rp ~ 70°. Here after, the zonal belt 20° ~ rp ~ 45° will be shortly

referenced as the southern area, and the zonal belt 45° ~ rp ~ 70° as the northern area.

The surface atmospheric temperature anomaly distributions in the two areas (Fig 3.5 d)

show some similarities. The decadal mean anomalies are predominantly positive in the

both regions in early 1950s and negative in the 1970s. The temperature anomalies in the

two areas (southern and northern) show a warming trend at the end of the study period

from 1995 to 2005. In the southern region (blue line) this trend starts in the late 1980s

while in the northern region (green line) it begins later- in the second half of the 1990s.

The spatial distribution of the atmospheric temperature anomaly averaged for three

periods of time : (a) from 1950 to 1960, (b) from 1970 to 1980 and (c) from 1995 to 2005

are shown on Fig 3.5 a, b, c. The first period 1950-1960 (Fig 3.5 a) was relatively warm

in the Western North Atlantic. The pattern of the highest atmospheric temperature

extends along the Gulf Stream area, the Labrador Sea and off east coast of Greenland.

Negative atmospheric temperature anomalies are observed in the zonal belt between 20~

and 30~ and along the Western North Africa and Western European coasts.

The cold atmospheric temperatures during the 1970s dominate in a zonal region of the

North Atlantic between 30~ and 55~, in the Northern Labrador Sea and along the

Northwestern Africa coast. Slightly positive anomalies are observed in the rest of the

North Atlantic. The comparison of Fig 3.5 with Fig 3.2 suggests that the mid-latitude

areas of strongest warming in the 1950s and cooling in the 1970s approximately

coincides with the mid-latitude area of westerlies. In the tropical areas where the

52

dominant winds are passats, the anomalies were negative in the 1950s and close to zero in

the 1970s. In the late 1990s the atmospheric anomalies are positive almost in the whole

North Atlantic with the exception of a small region in the Caribbean basin.

The wind anomalies in the northern and southern areas are clearly anticorrelated during

the period from 1948 to 1995 (Fig 3.6 d). From 1950-1965 the zonal westerlies in the

northern area tend to decrease, while the zonal wind anomaly increases in the southern

sub-region. During the rest of the period until 2005, the wind interannual variability is

opposite in the two regions. The reason for this anticorrelation between winds anomalies

in the sub-regions, which is discussed in more details in the next chapter, are related to

the variability of the North Atlantic Oscillation (NAO).

The zonal air mass transport is an important factor for the air-sea interaction over the

North Atlantic. Intense zonal winds bring relatively dry air from the continent over the

ocean. The weakening of the zonal winds off the coast ofNewfoundland in the 1950s is

related to weakening of storms and cold air masses transport in this area.

Correspondingly the winter of 1950s were warmer than usual in this part of the North

Atlantic. In opposite the westerlies were stronger than usual in 1970s (Fig.3.6.b). The

winters of 1970s were correspondingly colder than usual at mid-latitudes (Fig.3.5.b).

However, the comparison of (3.5c) and (3.6c) shows that this relation between the zonal

wind and TA anomalies is not always present.

In the 1990s the zonal wind anomalies in the whole North Atlantic show overall increase

in the intensity of both system- westerlies in the mid and polar latitude, and easterlies in

53

a)Period 1960 ·1960 b) Period 1911) ·1960

d) Zonal Wind anomaly c) Period 1995 • 2005 3.---~--~--------------~----,

2 2

t t

0 • ·1 ·1

Fig 3.6: lntcr·Annualand lntcr·Decadal Variability of Wind

54

the tropics. One would expect that the intensified transport of continental cold and dry air

would intensify the heat loss in the both areas. TA (Fig 3.5) and SST anomalies (see

below) however are both positive over the main part of the basin. This presumably may

be explained by the fact that there are other factors beyond the zonal transport, which

influence the surface atmospheric temperature distribution during this period. Two of the

most important factors which remain beyond this study are radiative fluxes and

meridional transport. They are the major 'candidates' which may be responsible for the

overall warming of the North Atlantic.

Fig 3.7 of SST anomalies clearly show presence of three periods in the North Atlantic

SST variability. The SST anomalies are in general positive in the 1950s and negative in

the 1970s. After 1995, the SST anomaly increase until the end of the period which is

2005. The patterns of SST in the 1950s, 1970s and in the 1990s are very similar with the

pattern of TA , suggesting that the variability of these two parameters is strongly

connected.

The net heat flux (Fig 3 .8) exhibits more complex variability than the parameters

discussed so far. The net heat flux depends in a complex way on TA, SST and wind

speed. The variability of all these parameters together with atmospheric humidity

influences the net heat flux. In the 1950s the net heat flux is predominantly positive in the

almost whole North Atlantic except the area of Gulf Stream and North Atlantic current.

55

a) Period 1950 -19«10 b) Period 1970-1980

01 .(1.8 .0.4 .0.2 0

d) Sea Sulface T~re ....,aly c) Period 1995-2005

0 0

OJ .0.& .(1,4 .0.2 0 0.4 0.8 0.8

f'ig 3.7: Inter-Annual and lnter-De.:adal Variability of SST

56

In the 1970s the heat flux is predominantly negative with exception of the Gulf Stream

area and a area off the coast of Western Europe. In the 1990s the heat flux anomaly in

tropical and subtropical North Atlantic is positive. In the areas of deep-water formation in

the Labrador and Greenland Sea the heat flux is negative. In the northern Labrador Sea,

there is an area of positive heat flux anomaly, which however is relatively small. The

spatial mean of the heat flux anomaly in the 2000 (Fig 3.8 a) is positive in the southern

and negative in northern area.

The analysis of seasonal mean and anomalies of the surface atmospheric characteristics

and SST suggest that there are distinct patterns of ocean-atmosphere relationship

associated with interannual variability. The middle and high latitude SST and TA display

a long term fluctuations with positive anomalies in the 1950s and 1990s and negative

anomalies in the 1970s. The zonal wind anomalies are negatively correlated in middle

and low latitudes. The patterns in the zonal wind show some relation with the SST and

TA anomalies in the mid latitudes in the 1950s and in the 1970s. In the 1990s this relation

is less evident. In this period the turbulent net heat flux is predominantly negative in the

polar areas and positive in the low and middle latitudes.

57

a) Period 1960 • 1960 b) Poriocl1970-1980

• 0 10 " 20

c) Period 1995 • 2005

0 0

~ ·15 .to 0 10 20 .,,.. ..., "" "" "'' ... .,., .,f

Fig 3.8: Inter-Annual and lnter-Decadal Variability of Total Heat Flux

58

Chapter 4

Empirical Orthogonal Function Analysis of SST and Atmospheric Data

The aim of Empirical Orthogonal Function (EOF) analysis is to determine the principal

modes of variability of the studied data. Empirical Orthogonal Function analysis is a

decomposition of a signal or dataset on to orthogonal basic is of functions, which are

determined from the data. EOF method finds both time series and spatial patterns (see

Chapter 2). Once the eigenvectors are found, it is important to separate those

eigenvectors (or EOFs) which contain data that represent physically relevant patterns

from those that represent only noisy variations. It has also been noticed that in analysis of

this type, the eigenvalues fall exponentially and most of the variability is captured only

by very few vectors.

The data used in this study are time series of monthly mean anomalies of SST and

atmospheric data in the North Atlantic and Labrador Sea for winter months (DJF) of the

period between 1948 and 2005. The SST fields are taken from COADS data set

(Woodruff et al., 1987) and have a horizontal resolution of 2 degrees. The atmospheric

parameters are from National Center for Environmental Predictions (NCEP). The

analysis covers the North Atlantic sector north of 20~. At each grid point the anomalies

have been calculated by subtracting the long term monthly mean.

59

4.1 Dominant modes of variability of the North Atlantic atmospheric

circulation and NAO from 1948 to 2005

The first EOF of sea level pressure (SLP) of North Atlantic, explains 44% of the total

variance present in the original data. The large positive values centered around latitude

45° N and the large negative values centered around 65° N are indicative of two regions

whose mean sea level pressures are generally inversely related. This EOF defines a

pattern which is a well-known low-frequency atmospheric circulation pattern called the

North Atlantic Oscillation (NAO). The NAO is characterized by large-scale SLP

variability associated with a subtropical high I polar low system over the Northern

Atlantic. During a positive NAO, (positive values on Fig 4.1 b) the subtropical high is

stronger than usual and the polar low is deeper than usual. The increased pressure

gradient causes stronger winter storms to cross over the Atlantic. During a negative

NAO, the subtropical high and polar low are both weaker than usual, resulting in fewer I

less severe storms crossing the Atlantic.

The intensity of the NAO is usually studied by using the so-called NAO index, which is

the normalized difference of pressure anomalies over Iceland and Portugal. This

characteristic can be calculated for the last 200 years, because SSP data for these two

stations are available for this period of time. The SSP analysis data, which we use in

these calculations, are available for not more than 50 years. Though such data do not

allow analyzing a long enough sequence of temporal variability of SSP, they provide

much better information about the spatial variability of SSP than the two point

observations (Portugal, Iceland) only.

60

There is a wide range of atmospheric and ocean variability attributed to the changing

NAO, which have the potential to cause change in the marine environment. In particular

in many studies during the recent two decades, it was shown that processes of water mass

formation in the North Atlantic are related to the NAO. The radical interannual and

interdecadal changes in the production of the convectively formed mode waters of the

West Atlantic, which Dickson et al.(1996) suggest to be a part of a coordinated pan­

Atlantic pattern of convective activity, driven by the changing NAO. From the late 1950s

to 1970, a regime of cold winter air temperatures and extreme snowcover greatly

enhanced the land-sea temperature gradient at the US eastern seaboard, spinning up more

storms than normal offshore (Dickson and Namias, 1976; Hayden, 1981). The local effect

was to focus the center of maximum storm activity off the US eastern seaboard where the

cold stormy conditions caused maximum cooling the ocean surface (see Fig 3.5b and

3.7b) and formation and ventilation of the Eighteen-Degree. The remote effect was to

reduce storminess over the Labrador Sea, so that Labrador Sea convection became

increasingly suppressed and fresh water built up at the surface (Lazier, 1980, 1988,

1995). Labrador Sea Water (LSW) production resumed abruptly in winter 1971-1972

with a rapid removal of the surface fresh water accumulation by the vertical spreading as

the cold winter regime ended at the US east coast and intense, chill northwesterlies and

storminess returned to the Labrador Sea. Later the tendency has been towards

intensifying and deepening ventilation of the Labrador Sea, with a progressive cooling

and freshening of LSW during the period of the 1990s. The LSW density increased as

convection began to produce cold but saline sublayer of North Atlantic Deep Water

(Dickson et al., 1996). This variability in the LSW formation is related to the changes in

61

the atmospheric characteristics driven by the NAO. From the 1950s the EOF1 coefficient

(Fig 4.1b) has decreased from positive to its lowest (negative) value for the whole period

1948-2005, which occurred in the 1960s. This period was the period of low storm activity

in the North Atlantic and was characterized by high Atmospheric and surface ocean

temperatures (Fig 3.5, Fig 3.7).

The connection between the ocean variability and NAO was however different in the

1990s. It is known that the NAO had a tendency to be positive since the late 1980s. This

is the period when NAO had its highest intensity (see Fig 4.1b) for the whole period

1948-2005. The SST during this period (see Fig 3.7a) showed a strong tendency towards

increasing. This tendency started earlier (in 1990) in the southern region (southern of 45°)

and later (in 1995) in the northern region. The low correlation ofNAO and SST suggests

that beyond the direct air-sea interaction, there was probably another factor, which

influenced the SST variability in the 1990s. As mentioned in introduction of Chapter 3 an

important factor for the thermal regime of the North Atlantic is the ocean circulation. The

long term variability of the ocean heat transport however remains a challenging problem

due to the lack of data. The most important contributors to the meridional transport are

Gulf Stream and North Atlantic Current.

As Curry and McCartney (200 1) point out, the main North Atlantic Current is driven by

the gradient of potential energy anomaly (PE) across the mutual boundary between the

subtropical and subpolar gyre. Since P E reflects the vertical density structure and heat

content of the upper ocean to well below the wind-driven layer, it follows that

coordinated changes of opposite sign in the production and characteristics of the mode

waters in each gyre will have the potential to drive deep-seated changes in the P E

62

gradient, and hence in the strength of Atlantic gyre circulation. If these changes in the

density and heat content of mode waters are attributable to the NAO, then the

amplification of the NAO to extreme values over the past three or four decades is likely

to have been followed by a corresponding multidecadal spin-up of the Atlantic gyre

circulation.

From the observed PE differences between the centers of the two gyres, Curry and

McCartney calculated that the long term increase in the NAO index to the mid 1 090s was

accompanied by a 30% increase in the east going baroclinic mass transport along the

gyre-gyre boundary. Both subpolar and subtropical gyres contributed equally to the

changes in their transport index. Thus in response to the NAO, the North Atlantic gyre

circulation during the early 1990s is likely to have been at its strongest for more than a

century.

The second EOF of SLP over North Atlantic exhibits 27% variance, which is called the

Eastern Atlantic (EA) pattern (Barnston and Livezey, 1987). The EA is related to an

atmospheric pattern with low-pressure center at about rp = 55° N and A = 25° W, which

is inversely related to the SLP in the rest of the North Atlantic.

63

(b) Ttne 111111es SI.P EOF 1 (a)Sea Surface Pressure EOF 1 variance: 0.44487

1960 1970 2000

(d) Time series SLP EOF 2 (c)Sea Surface Pressure EOF 2 variance: 0.27048

0.5

0

~.5

·1 ~.08 ~.07 ~.06 ~.05 ~.04 ~.03 ~.02 ~.01 0 0.01

1990 2000 2010

Fig 4.1: Dominant EOFs ofSea Level Pressure and their time series (red curve is the

filtered time series) of North Atlantic.

64

4.2 EOF analysis of near surface atmospheric parameters and SST

EOF Decomposition is applied to Air Temperature of North Atlantic (Fig 4.2). The first

structure explains 51% of the variance, the second structure 13%, and the third EOF

explains 6%. The first EOF has triple structure with positive values of the US coast and

opposite negative sign in the Labrador Sea and tropical North Atlantic. The time

variability (Fig 4.2b) follows closely the NAO index.

We have compared our results with the results of Deser and Blackmon (1993 ). The first

two EOFs of air temperature are similar with the pattern of SST EOF, just the order of

mode is reversed. The second EOF of air temperature, which accounts for 13% of the

variance, exhibits maximum amplitude off the Newfoundland, North Labrador Sea and

off the coast of east Greenland. The time series of EOF2 is dominated by along warming

trend from the 1950s to the 1970s, followed by a cooling trend during 1970s and 2000s.

65

(c)--.--~ 2 (ooo0.1S167)

•M•r------~"'!-~ _., ... _, ·--:·---~---

•

-~·r~------!,.~-~"-~-~---.o;---co"~

"

~l .,_ ' ·-

• ·•

-

. ·-

-

. ··~

. ·- . ·- -=·~--=

til,_- .. • .. , - eooo•

: '

- - - ·- -Fig 4.2: Dominant EOFs of air temperature ant/their time series (red curve is the

filtered time series) of North Atlantic.

66

-

The dominant SST is shown on Fig 4.3. The first normalized eigenvalue is 0.23, the

second eigenvalue is 0.18, and the third eigenvalue is 0.14. Recall that normalized

eigenvalues represent the fraction of variance explained by the structure associated with

that eigenvalue. Therefore, the first EOF structure ofNorth Atlantic Ocean explains 22%

ofthe variance, the second structure 17%, and the third EOF explains 13%.

The SST dominant EOFs define patterns, which are pretty similar to the EOFI and EOF2

of the heat flux (see below). The EOFI identifies two areas of opposite variability. The

first is southeastern of Newfoundland and Labrador Sea and second is the subtropical

North Atlantic and Gulf of Mexico. This structure is very close to the structure of the

EOF2 of heat flux. The time variability of EOFI is different from the EOFs discussed so

far. Though it shows some variability at interannual time scale, there is a stronger

changes in this EOF at decadal time scale. The coefficient of this EOF is predominantly

positive from 1950 to 1970, negative from 1970-1990 and positive in 1990s.

The second EOF defines a triple with two areas in subtropical and subpolar North

Atlantic, where SST anomalies due to EOF2 are opposite to those in Gulf Stream Area.

This pattern is known (see Cayan, 1992) to be strongly correlated with the NAO.

Correspondingly the time variability of the EOF2 coffecient vary in a similar way as the

EOFI ofSLP.

67

00 s--..r.c.T.....,....,.eOF 1 (cr •02214) .. • • • -~

-~,,_,_-,,._,..-,,c._..---...- . ·-. ·- . - -· .. .,..._ _ _. ___ IIO<i't

.. • • • ...

.. Q'IT-._., ____ _

... •

• • ... .. ,_ ·- ·- - ·- ·- - -

Fig 4.3: Dominant EOFs o/SSf and their lime series (red cun•e is lhe filtered lime

series) of North Allanlic

Deser and Blackmon (1993) have done an EOF analysis of SST in the North Atlantic.

They have found the first EOF of SST, which accounts for 45% of the variance, has

uniform polarity over the entire basin. The largest loading occurs along the Gulf Stream.

The time series of EOF1 SST exhibits a sudden transition from below normal values to

above normal values around Second World War. This EOF was not found in the present

study and also in the work of Cayan (1992).The technique for measuring SST was not

accurate before early 1940s. As also discussed by Deser and Blackmon, the EOF1 is

probably related to the change of technique of SST observation.

The second EOF which accounts for 12% of the variance, exhibits a center of action east

of Newfoundland at the boundary between the subtropical and subpolar ocean gyres.

They have found an opposite polarity located off the southern United States. The time

series of EOF 2 exhibits quasi-biennial fluctuation and also quasi-decadal variations. We

have also found similar results in our EOF and also the time series is similar after 1948 to

onward.

69

Fig 4.4: EOF analysis of SST from 1900-1989. (Deser & Blackmon)

There is also a possibility that interannual and decadal fluctuations in SST are response to

ocean and atmospheric variations outside of North Atlantic. Deser and Blanckmon,

(1993) have found a link with the sea ice transport in the Davis Strait-Labrador Sea

region. Figure 4.5 a) shows the time series winter sea ice concentration anomalies in the

Davis Strait-Labrador Sea. The circle denotes the winter anomaly, plotted in the year in

which January occurs. The solid curve shows the data smoothed with a three point

binomial filter. Decadal variability is evident in the sea ice record, with peaks occurring

in the winters of 1957/58, 1971/72, and 1983/84. Figure 4.5 b) shows the sea ice record

superimposed upon the time series of the second EOF of winter SST. ( Deser &

Blackmon, 1993)

It may be seen that the maxima in sea ice concentration precede the minima in SST by 1-

2 years. There is a strong lag in correlation between the two time series. This indicate that

on the decadal time scale, winters of heavy sea ice in the Labrador Sea precede winters of

colder than normal SSTs east ofNewfoundland. It is probable that the sea ice anomalies

70

in the Labrador Sea are advected southwestward, resulting in colder than normal SSTs

east of Newfoundland the following year. Thus the quasi-decadal cycle in SSTs east of

Newfoundland may result in part low-frequency Arctic sea ice variations.

40

20

.... 2 0

,, :·

f\1 :·t\r.l.

J \.'

-2~9~~~~~~~~~~~~~~80~~ ~

b

{b)

Fig 4.5 a) Time series of Winter Sea ice area anomalies in the Davis Strait and Labrador

Sea region. b) Standardized sea ice anomalies from super imposed upon the standardized

time series of EOF2 of North Atlantic winter SST (after Deser and Blackmon, 1993)

The dominant EOF mode of wind (Fig 4.6 a) explains 46% of the variance and the

second EOF explains 24% of the variance. The dominant EOF defines a pattern which

has a dipole structure with opposite variability in the sub-polar and sub-tropical regions.

This EOF, which dominates the zonal wind variability, explains in particular the

anticorrelation between the winds anomalies southern and northern of 45~. The pattern

related to the EOFl constitutes oscillations with opposite phase in these two regions. It's

time variability follows closely the NAO index.

The second EOF in the wind defines a triple pattern. The variability related to this EOF in

the wind in the mid-latitude area between 30~ and 55~ is opposite to that in the

subpolar and tropical North Atlantic.

71

" " * H

• -~

--.... _ ·--* N . • --.... -

.

010 __ , ___ ,

·- - ·- ·-"'.,__ .. __ COOl'. . .

·- • ·-•r------------~~,._,-,=~ .. --cOl''

• ... -

- -·

-

., .. ~---, ..... -.---,HM .. .---,,c,,.H;---;.,.-..---,, ..... ---. ..... .---.1 ...

Fig 4.6: Dominant EOFs of Wind and their lime series (red cun-e is I he jillered time

J·eris) of North Atlamic.

n

The first EOF of precipitation (Fig 4.7 a) of North Atlantic which explainsl6% of the

variance has highest precipitation rate in the northern coast of Newfoundland and US

coast and lowest in the southeastern part of North Atlantic. The second EOF, which

explains 14% of variance has highest precipitation rate in Gulf Stream and lowest in

central Atlantic. The third EOF of which explains 7% of the variance has highest

precipitation all over the Atlantic.

The first three EOFs in total precipitation explain only about 40% of the total variance.

The rest of the variance in the precipitation anomalies is due to the higher EOFs. In this

way, we need relatively large number of EOFs in order to spawn the precipitation

variability. The first EOF coefficient has a time variability, which follows closely the

variability of the SLP EOF1 coefficient. This is the pattern closely related to the NAO.

The dominant EOF mode of total heat flux explains 21% of the variance and the second

EOF explains 15% of the variance. The third structure explains 8% of the variance. Fig

4.8 shows the dominant EOFs for the surface net turbulent flux. The first EOF (Fig 4.8 a)

defines a pattern of alternating anomalies in the areas of subtropical and subpolar ocean

gyres. The low-pass filtered time variability of this EOF follows closely the time

variability of the first SLP EOF defining the NAO pattern. The second EOF defines a

pattern in the heat flux with alternating anomalies in the region southeastern of the

Newfoundland and the rest of the North Atlantic.

73

.. , .. ---- -· (.ol) T - ~lloeoft llQIO 1(0040.1~7:3)

' • •

' f ,~

• ·- . . . ..:.. ·- - "" ·- ·- -· ..... ___ ,_ -· • •

•

• ~ .,_ - ·- - ·- --- - -... ,,. ~,__ ___ .... ,I ..

.. •

••

•• . 1.:.. - ·- - ·- - - •

Fig 4. 7: Domlmmt EOF of Preclpllallon Rate and their time J·erles(retl curt't iJ the

fi/t~n-~1 wne series) of Atltmnc.

74

.,__, ____ . --• --- - - - - - - -

.___.., ____ , 1 ---

• v --- - - - - - - -t•) ~ ..... lbl: EOF 3 (-O.Dit0012) - ___ .. ____ .

--·-• --- - - - - - - -

FIR 4.8: /)Qminant EOFs of Total lleot J.1u.Yand their time serle\' (reel curve i.v the

filteml time serle<) of Atlantic.

7S

These results correspond to the findings of Cayan (1992). The total heat flux differences

associated with positive versus negative extremes of the first two North Atlantic SLP

EOFs are shown in Fig 4.9 and corresponding MST' I M differences are shown in Fig

4.1 0, which is the quantity of thermal energy transferred across a unit area of Sea Surface

per unit time. SST anomalies fall in regions of positive sea-to-air flux and rise in regions

of negative flux. In concurrence with the NAO circulation pattern, the North Atlantic is

partitioned into alternating anomalous cells: 1) positive MST' I M differences in the

northeastern North Atlantic between Great Britain and Scandinavia; 2) negative

!).SST' I M differences in the central North Atlantic southeast of Greenland between 50~

and 60~; 3) a broad region of positive MST' I M differences extends from the Gulf of

Mexico and the eastern seaboard east to the central Atlantic at about 350N,300W; 4)

negative MST' I M differences occupy the eastern tropical North Atlantic between about

500W and North Africa. The major regions of impact of MST' I M are closely

harmonized to those of total heat flux, supporting the view that they are linked.

For the North Atlantic SLP EOF2 (EA), the major MST' I M features are 1) negative

differences in the central North Atlantic east of Newfoundland; 2) positive differences in

the Gulf of Mexico and the region just east of Florida and 3) positive differences in the

far northeastern Atlantic and the Mediterranean Sea.

There is a difference in the pattern defined by the EOF2 of heat flux (Fig 4.8c) and the

corresponding pattern of Cayan (1992). The pattern on (Fig 4.8c) is shifted south­

westward and is more extended towards the US coast in the Southern part. This

difference may be attributed to the different method used by Cay an ( 1992), which

considers the heat flux distribution during years of extremely high or extremely low

76

NAO. In this way the patterns of Cayan (1992) represent the structure of most anomalous

(in terms ofNAO index) years.

Fig 4.9: Difference of average total heat flux associated with positive vs negative extreme

winter month ofNorthAtlantic SLP EOFJ and 2 of (Cayan 1992)

77

Fig 4.10: Difference of average thlST' I M associated with positive vs negative extreme

ofEOFJ and 2 ofNorthAtlantic SLP. (Cayan 1992)

78

The dominant EOFs in the near surface atmospheric characteristics and SST define

patterns show close connection to the global atmospheric circulation. The EOF analysis,

for the period 1948-2005 in correspondence with previous studies, indicates that the

NAO has an impact on the North Atlantic Ocean and atmospheric variability. The EA is

another important pattern for the North Atlantic. At the same time it is known that

internal ocean variability may also influence the atmosphere and SST. The next chapter

studies the connection between the variability in the North Atlantic Ocean and Labrador

Sea, and the atmospheric circulation.

79

Chapter 5

Canonical Correlation Analysis

The anomalies of heat and water exchange between the atmosphere and the Labrador Sea

depend on the variability of wind speed, the ocean surface saturation humidity, air

humidity and the sea-air temperature difference. These parameters define the intensity of

evaporation and the net turbulent heat flux at the ocean-atmosphere interface. Their local

values depend on the atmospheric circulation, which defines the intensity of the surface

wind speed and the direction of air masses transport. During the winter, the dominant

transport is directed from the continent towards the ocean and brings cold and dry air to

the ocean surface. The heat and water exchange depends on the intensity of this flow,

which is part of the atmospheric circulation

This section presents results from a study of the relation between the atmospheric

circulation, and near surface atmospheric variability and SST. The time variability of SLP

dominant EOFs discussed in the previous section show some qualitative relation to the

EOFs in other atmospheric characteristics (zonal wind, heat flux, atmospheric

temperature) and SST. This relation was shortly discussed in previous section. For

instance, negative SLP anomalies are related to negative zonal wind anomalies to their

north and positive zonal wind anomalies to their south. The analysis of this relation in

chapter 4 was just qualitative. Here the method of canonical correlation analysis is used

to study the relation between the near surface atmospheric characteristics and SST with

the atmospheric circulation variability. Section 5.1 presents results for the North Atlantic.

80

The relations of the near surface atmospheric characteristics and SST in the Labrador Sea

to the atmospheric circulation is discussed in section 5.2.

5.1 Correlation Patterns of Variability in the North Atlantic

Canonical Correlation Analysis (CCA) is used to analyze the relationship between

monthly mean sea level pressure (SLP) or sea surface pressure (SSP) and atmospheric

temperature, wind, heat flux, SST, precipitation in the North Atlantic. The data are time

series of monthly means of SLP and atmospheric temperature, wind, heat flux, SST,

precipitation grided over the North Atlantic north of about 20~, for DJF of 1948 to 2005

respectively. Anomalies are obtained at each grid point by subtracting the long term

monthly mean from the original values. The CCA yields two pairs of patterns that

describe the coherent variations in the two parameters.

The first pattern (Fig 5.1 b) of SLP and SST corresponds to a canonical correlation of

84% that means the areas of strong coupling of SLP with SST indicated by 84%. The

coefficient of the second pattern (Fig 5.1d) is 68%. The coefficient of the third pattern

(Fig 5.1 f) is 58%. The first pattern (Figs 5.1 a, b) of SLP exhibits the pattern similar to

NAO pattern which drives the variability in the SST close to the 2nd EOF and second

mode of canonical correlation pattern of SLP describes EA pattern which drives the

variability in the SST close to the first SST EOF. These results correspond to the studies

of Cayan., (1992) and Deser et al., (2000). These studies in particular relate the second

EOF (Fig 4.5), or triple pattern in SST anomaly field with the NAO. The first EOF in

SST, defines a pattern that is close to the one derived by Cayan (1992) and driven by

Eastern Atlantic pattern in the atmospheric circulation.

81

The third correlation pattern of SLP and SST (Figs 5.1 e, f) has a SLP structure close to

the NAO but with a maximum in the SLP field shifted westward. This canonical

correlation pattern in the SST has a dipole structure with opposite variability in the

subtropical and subpolar gyres.

The first pair of patterns SLP and atmospheric temperature corresponds to a canonical

correlation of 90% of the SLP and air temperature. The correlation coefficient of the

second pairs of patterns is 85%. First canonical pattern (Figs 5.2 a) of SLP is North

Atlantic Oscillation (NAO) and drives the variability in the air temperature close to the

first EOF. The second mode (Fig 5.2 c) of canonical correlation is a combination between

NAO and Eastern Atlantic (EA) pattern that drives an air temperature anomaly close to

the second EOF. These two patterns show how the variability in atmospheric circulation

influences the near surface atmospheric temperatures as discussed in Chapter 1. High

NAO index is related to an intensified cyclonic vortex in the Icelandic low. The mean

transport in the Labrador Sea favors north-eastern cold winds. The winter storms are

passing across the Atlantic Canada and cause low temperature off Newfoundland. The air

temperature off the coast of US is warmer than usual.

The shift of the centers of low northward of Iceland and of the high northwestward of

Azores Islands in the NAO shifts the areas of high and low temperature in the second

canonical correlation patterns northward (Fig 5 .2d).

The first pattern of SLP and zonal wind (Fig 5.3 b) corresponds to a canonical correlation

of99.97%. The coefficient ofthe second pattern (Fig 5.3 d) is 99.90%. The coefficient of

the third pattern (Fig 5.3 f) is 99.61%.

82

The first two dominant SLP-zonal wind patterns (Figs 5.3 a, c) are related with the NAO.

In the first pattern the high in Eastern Atlantic is shifted northward of the Azores Island.

In this case the zonal wind is intensified in the eastern part ofNorth Atlantic off the coast

of England. The zonal transport is weaker than normal in the subtropical North Atlantic

Ocean.

The second SLP pattern (Fig 5.3 c) has a structure of the NAO with the low shifted south

of Iceland. Correspondingly the area of intensified zonal winds moves southward with

respect to the first pattern. The strongest zonal transport related to this pattern is between

Newfoundland and Western Europe. The third canonical correlation pattern (Fig 5.3 e)

has a structure of the Eastern Atlantic pattern in the SLP. It is known (Barnston and

Livezey, 1986) that the low related toEA pattern can move zonaly in the North Atlantic.

In canonical correlation pattern three, this center is shifted westward with respect to EOF

2 of SLP. During the positive phase of this pattern, the zonal wind intensify in the

tropical North Atlantic and off the west coast ofEurope.

The first patterns of SLP and heat flux (Fig 5.4 b) corresponds to a canonical correlation

of99.8%. The coefficient ofthe second pattern (Fig 5.4 d) is 99.45%. The coefficient of

the third pattern (Fig 5.4 f) is 99.09%. The fourth pattern of SLP and heat flux

corresponds to a canonical correlation of 98%. First canonical pattern of SLP is NAO

which drives the variability in the turbulent heat flux close to the first EOF of the heat

flux. The second and third SLP modes (Fig 5.4 c, e) of canonical correlation are similar

to the Eastern Atlantic (EA) pattern which drives the turbulent heat flux anomalies close

to the second EO F.

83

The first patterns of SLP (Fig 5.5 b) and precipitation corresponds to a canonical

correlation of 9 5% of the variance of SLP and wind. The coefficient of the second pattern

(Fig 5.5 d) is 93% of the variance of SLP and precipitation in the North Atlantic. The

coefficient of the third pattern (Fig 5.5 f) is 92% of the variance of SLP and heat flux in

the North Atlantic. The fourth pattern of SLP and precipitation corresponds to a canonical

correlation of 87% of the variance of SLP and precipitation. First canonical pattern of

SLP (Fig 5.5 a) is North Atlantic Oscillation (NAO) which drives the variability in the

precipitation close to the first EOF. The second mode (Fig 5.5 c) of canonical correlation

is similar to the Eastern Atlantic (EA) pattern, which drives the precipitation anomaly

close to the second EOF.

84

·- - - -

Fig 5.1: Upper two panels .show tltejir,fl Canonical L'Orre/alion J)llllernfor (t1) SLP or

SSP (b) SST 11/tld/c two panels show th<t second CC pattern/or (c) SLP (d) SST. f.ou·er

tuo panels showth<t third CC poiternfor (e} SLP (d) SST.

cc.- t: ... _OcoonSLP-

.. ... ·U 0 0.1

Fig 5.2. UpfJeT two /l('nel< show I he firs/ CC /l('llemfor (a) SLP (b) air lemperlllllre.

Lower two panels show the second ('("pattern/or (c) SI~P (d) llir temperature

86

Fig 5.3: Upper lwo panels show the firs/ Canonical correlalion p<lllem}Or (a) SLP (b)

zona/wind J\tliddle lwo fXInels show the second CC pallernfor (c) SLP (d) zonal wind

Lower lwo JXmels show the third CC fXlllem}Or (e) SLP (d) zonal wiml.

87

co-, ...... ,,,. ..... ._.,.._..

•

Fig S.4. Upper r.·o pun</$ shou IM fiT!/ Cononico/ correlallon pull<rn/Ot" (a) S/.P (b)

ltet~tfl•u:. Middle two panels show the ;econd CC pullernfor (c) SLP (d) heat flux. Lower

r.•o panels show the third CC pallernfor (e) SLP (d) hcOij/liX.

II

oo_., _ _ _

oo-·-- ..-.

Fig S.S ~"pfwr lln> pan< Is show tlw fmt Canonirol corr./Diion pallmr/or (a) SLP {b)

fNrclpilution rot~. MilitO~ n.o ponrls show t- s~rond C( pilll~rnfor (c) SLP (d)

precipitation rate. Lower t-..·o pcmt!l.J show the third CC palftrnfor (e) SLP (d)

J'redplfation rate.

19

5.2 Correlation Patterns of Variability in the Labrador Sea

In this section CCA is used to study the relationship between monthly mean sea level

pressure (SLP) North Atlantic and atmospheric temperature, wind, heat flux, SST,

precipitation in the Labrador Sea. The data are time series of monthly means of SLP and

atmospheric temperature, wind, heat flux, SST, precipitation on a grid over the Labrador

Sea north of about 50~, for DJF of 1948 to 2005 respectively. Anomalies are obtained at

each grid point by subtracting the long-term monthly mean from the original values. The

CCA yields two pairs of patterns that describe the coherent variations of the atmospheric

temperature, wind, heat flux, SST and SLP fields and three patterns that describe

precipitation with the SLP fields. These patterns are dominant in describing SLP with

other parameters variance in the Labrador Sea.

The first pattern of SLP and SST (Fig 5.6 b) corresponds to a canonical correlation of

85%. The coefficient of the second pattern is (Fig 5.6 d) 72%. First canonical pattern of

SLP is North Atlantic Oscillation (NAO) which causes cold temperature in the Labrador

Sea with strongest impact in the northern part of the Labrador Sea and some part in the

southern area. The second mode of canonical correlation is similar to the Eastern Atlantic

(EA) pattern which has strongest impact on the northern part of the Labrador Sea.

The canonical correlation patterns are obtained through linear correlation analysis of SLP

and SST fields. The dominant patterns of CCA are well correlated in time and therefore

one can use them to predict the values of SST if SLP is known. Prediction of SST is

based on using canonical variates for SLP to project variability of SLP into

corresponding canonical correlation patterns of SST. The reconstruction of SST by using

SLP canonical correlation variates is given by Zorita et al (1992):

90

R " (t ) = " .f3 SLP (t ) fSST S5l n L..,. P1 1 n J 1 5.1

This approach is used in statistical weather forecasting methods. Some problems may

arise when the CCA is used to reconstruct one parameter (SST) from known values of

another (SLP). CCA patterns (Zwiers and von Storm, 1999) can not necessarily explain

all the variance of the SST. Following the terminology of Chapter 2, let us consider the

two parameters SST = SST d+SST', SLP = SLP d + SLP', each consisting of two

components - deterministic and stochastic. The canonical correlation analysis is based on

the correlation between SLP d and SST d represents variabilities in the two parameters

which are not correlated. The variance of SLP' and SST' define importance of factors

which are not considered by the CCA.

In the case of SST and SLP, the basic assumption of CCA is that atmospheric circulation

(SLP) variability influences the surface heat fluxes in the Labrador Sea, which are

important for the time changes of temperature in the surface ocean layer. Bjerknes., 1964

suggested this assumption is correct at interannual time scales, i.e. that interannual

changes in SST correlate well with the dominant modes of atmospheric circulation. This

is not the case, however, for the long term warming trends in the North Atlantic. In

chapter 3, it was shown that such trends are present in the North Atlantic in the 1950s and

late 1990s. Bjerknes (1964) suggests that the decadal trends of SST are related to the

variations of ocean circulation. The figure 5.7 shows water transport between Bermuda

and Bravo station. The green curve is NAO index filtered by 12 years and the black curve

is water transport and the red curve is SST anomaly. The NAO index (see Fig 5.7)

increase from 1980 to 1995. Water transport also increased during this period (Curry &

MacCartney, 2001 ). The SST trend in the 1990s is well correlated with the low pass

91

filtered NAO index and ocean transport. The major physical process responsible for this

long-term correlated trend in the three parameters is the ocean circulation. The transport

in the subtropical and subpolar gyre intensified after 1980 due to the NAO which is in

positive phase during the most of the time after 1980. The more intensive transport is

related to intensified heat transport in the surface ocean layer from the subtropics to the

subpolar region. Correspondingly the SST increases as a response to this transport. There

are two major properties of the SST, ocean transport and NAO variabilities during the

periods of positive SST trends, which are seen on Fig 5.7 and have impact on the quality

ofthe CCA and reconstruction of SST by using SLP:

1. The ocean transport responds with some delay to NAO. Moreover when the

meridional heat transport is intensified, during positive phase of NAO the time

required by a positive SST anomaly to propagate from the subtropical area to the

Labrador Sea is evaluated by Sutton and Allen (1997) as about 7-8 years.

n. The low-passed filtered variability in the NAO has variance much lower than the

variance ofNAO at interannual time scale see (blue and red bars on Fig 5.7)

The CCA patterns here do not consider an eventual time lag in the correlations between

the intensity of atmospheric circulation and SST. However if such time lag would be

considered, CCA will still not capture the correlation in the long term low pass filtered

trends between SST and SLP, because the filtered SLP trend has much lower variance

than the interannual variability in the nonfiltered SLP data.. Additionally the sea ice

variability in the Labrador Sea influences SST, introducing additional changes in SST,

which are not directly connected to the SLP variability. Fig 4.7 b shows the ice inflow to

92

the Labrador Sea through the Davis Strait has a strong impact on the dominant mode of

variability with a time lag of 1-2 years.

The CCA SLP-SST does not consider factors like ocean circulation, sea ice transport

which are important for the SST variability. Therefore one can expect that the

reconstruction of SST by using CCA patterns will not approximate perfectly the real SST

field. In order to assess the approximation skills of CCA reconstruction the following

parameter is used (Cayan, 1992):

(5.2)

which estimates the variance of SST explained by CCA patterns.

In Figure 5.6 (e) the blue line is the SST anomaly in the Labrador Sea and green line is

SST anomaly reconstructed by CCA. In this figure it is clearly shown that the SST is

weakly correlated with SLP and only in the cold period from 1970-1980s.

The variance explained by the CCA (Fig 5.6 f) is around 20% in the southern part of the

Labrador Sea. In the rest ofthe basin, the approximation skill is very negative. This result

shows that SST in the Labrador Sea is only weakly correlated with SLP patterns and the

variability of the atmospheric circulation. Strong impact on the SST in the Labrador Sea

have ocean heat and sea ice transport.

93

•• r--- _.,.. ___ .-T __ ._

•• •• •• .. •

••

·- ·- ·- - -· Fig 5.6: Upper two panels show the first (.(monica/ correlation pallemfor (a) SI.P (b)

SST. Middle two panels .vlrow tire second CC pallernfor (c) SLP (d) SST. e) Lower two

panels slrow SST anomaly (blue curve) and reconstructed SSt anomaly (green curve)

d) Variance of SST(%) explained by CC reconsrruclion

- bl!plrti'Qa 0-md! - ..... N() .... d!J'I

·-""' --Fig 5.7: Water transport index, intt~rated NAO inde:c (Curry and Mac:Cttrftrey. 2001)

and SST anomalies (Sl111on, Allen 1997)

The first pairs of pottems of SLP and atmoophcric tempen~tun: correspond$ to a canonical

correlation of 98o/o. ·n1e cocllicient or the second pairs of patterns is 96~o. First canonical

pottem ofSLP (l'i& S.8 a) which has strongest impact in the northern part of the Labrador

Sea is lhe No<th Atlantic Oscillation (~AO). The second mode of canomcal (fig S.8 c)

which has stronge:>t impact also in the nonhem part of the l.nbrador Sen i!; similar to the

Enstem Atlantic (EA) patlem. 11tc SLP and air tempcrnture in the Labmdor Sea are well

correlated. The variance explained by lhe CCA (Fi& S.8 f) is around 60''1.-80%

cvc;ry~·here except cc:nlral po.n of the Labrador Sea ~here the explained \ariance is

around 40'/o.

9S

The first patterns of SLP and wind corresponds to a canonical correlation of 99%. The

coefficient of the second pattern is 97%. First canonical pattern of SLP (Fig 5.9 a) which

has strongest impact in the southern part of the Labrador Sea and near Greenland is North

Atlantic Oscillation (NAO). The second mode of canonical correlation (Fig 5.9 c) which

has strongest impact near the Greenland coast is similar to the Eastern Atlantic (EA)

pattern. The SLP patterns and zonal wind in the Labrador Sea are well correlated. The

variance explained by the CCA (Fig 5.9 f) is around 80%-100% everywhere except in the

Davis Strait and some costal parts ofNewfoundland where no correlation is found.

The first patterns of SLP and turbulent heat flux corresponds to a canonical correlation of

97%. The coefficient of the second pattern is 95%. First canonical pattern of SLP (Fig

5.10 a) which has strongest impact in the southern part of the Labrador Sea and near

Greenland is North Atlantic Oscillation (NAO). The second mode of canonical

correlation (Fig 5.10 c) which has strongest impact also in the southern part of the

Labrador Sea is similar to the Eastern Atlantic (EA) pattern. The SLP and turbulent heat

flux pattern patterns in the Labrador Sea are well correlated. The variance explained by

the CCA (Fig 5.10 f) is around 60%-80% everywhere except Davis Strait, Hudson strait

and coastal part ofNewfoundland.

The first patterns of SLP and precipitation corresponds to a canonical correlation of 98%.

The coefficient of the second pattern is 97%. The coefficient of the third pattern is 96%

of the variance of SLP and heat flux in the Labrador Sea. First canonical pattern of SLP

(Fig 5.11 a) which has strongest impact in the northern part of the Labrador Sea and near

96

Greenland is North Atlantic Oscillation (NAO). The second mode (Fig 5.11 c) of

canonical correlation which has strongest impact also in the coastal part of Greenland is

similar to the Eastern Atlantic (EA) pattern. The SLP and air temperature in the Labrador

Sea are well correlated. The variance explained by the CCA (Fig 5.11 f) is around 60%-

80% everywhere except northern part of Labrador Sea and coastal part ofNewfoundland.

97

• r _;·-:!'!:' =-~·-~·:!~~-=-~::·~-- __ .. _ • •

• -· • •

Fig 5.8: Upper MO pone/s show the first C<monical correlation p(l{ternfor (a) SLP (b)

air temperature. Middle two panels show the second CC potternfor (c) Sl.P (d) air

temperature. e) Lower two panels show air temper(llure cmomaly (blue curve) and

reconstructed air temperature anomaly (green curve) d) Variance of air temperature rAJ

explained by CC reconstruction

98

r __ ,.:,..::•;:•:::-:::-;::::"-=-:=::-=::";:'='::-::;..:•::"=-~--, '

••

•• •

•• ·• ... •

I

' I'

fig 5. 9: Upper IWO ponels show the first Canonical correlation polternfor (a) SLP (b)

zonal wind. Middle two ponels show the second CC pattern for (c) SLP (d) zonal wind.

e) Lower two panels show zonal wind anomaly (blue curve) and reconstructed zonal wind

anomaly (green curve) d) Variance of zonal wind(%) explained by CC recon.slruction

~

y

M

• • • ... ... . ,...

~-----.......,-·-

....

Fig 5./0: Upper two ponels show the first Canonical correlation pollemfor (a) SU' (b)

heatji1L<. Middle rwo poneL< show the second CC pallemfor (c) SLP (d) heatj/1<r.

e)Lou:er two panels show heat flux anomaly (blue curve) and reconslructed heal flux

anomaly (green curve) d) Variance ofhealjlux r/oJ explained by CC reconslrucliOn

100

cc mode 1: the Lab s- Prate pattem CC mode 1: the AUantJc Ocean SSP pattem

CC mode 2: the Lab Sea Prate pattem CC mode 2: the AUantic Ocean SSP pattem

x10-e

1 x10-e Variance (%) explaind by the CCpatems

0.8

0.8

0.4

0.2

0

.0.2

.0.4

.0.8

.0.8

-1940 19!50 11180 1970 1980 1990 2000 2010

Fig 5.11: Upper two panels show the first Canonical correlation pattern for (a) SLP (b)

prate_ Middle two panels show the second CC pattern for (c) SLP (d) prate. e)Lower two

panels show precipitation anomaly (blue curve) and reconstructed precipitation anomaly

(green curve) d) Variance of precipitation (1/o) explained by CC reconstruction

101

Chapter 6

6. Conclusions and Future Work

EOF and CCA are techniques commonly used in analysis of geophysical data. In this

study the application of these two statistical methods are used to study interannual and

interdecadal variability of Labrador Sea. The purpose of this study is to find the dominant

modes of variability in the North Atlantic SST and near surface atmospheric parameters

and to asses the effect of the atmospheric circulation on the SST and the atmospheric

parameters in the Labrador Sea and the North Atlantic.

• The SST and near surface atmospheric parameters are studied for the period of

time 1950- 2005.

• The data used m this study is Comprehensive Ocean-Atmospheric Dataset

(COADS). The SST data are used from this COADS dataset. And the other

parameters are taken from NCEP reanalysis.

• The dominant modes in the North Atlantic interannual variability are found by

using EOF analysis

• The dominant modes of interannual variability in the Labrador Sea and their

relation to atmospheric circulation are studied by using CCA.

• The approximation skills of canonical correlation patterns of SST, zonal wind,

turbulent heat flux, air temperature and precipitations are computed. The CCA

SLP-SST does not consider factors like ocean circulation, sea ice transport that

102

are important for the SST variability. Therefore it can expect that the

reconstruction of SST by using CCA patterns will not approximate perfectly the

real SST field. In order to assess the approximation skills of CCA reconstruction

the following parameter is used (Cayan, 1992):

Ji = [1- Lk (RSST (t n)- SST(t n )) 2 / Lk (SST(t n )) 2

] * 100%

which estimates the variance of SST explained by CCA patterns.

• The winter SST anomaly in the Labrador Sea especially during warm periods

does not show significant correlation with the patterns of atmospheric circulation.

• This result supports Bjerknes (1964) conclusion that decadal variability of SST

during warm periods depend mostly on non-local processes of horizontal transport

and less on the local heat exchange with the atmosphere. Inter-decadal warming

of SST in the North Atlantic is linked to the basin scale interaction. The Gulf

Stream and the North Atlantic current respond to the intensifying circulation in

the anti-cyclonic gyre.

• The near surface atmospheric parameters show good correlations with SLP.

From the results presented in Chapter 5 it follows that the future analysis of the climate

variability in the Labrador Sea should be based on additional data about variability of the

Atlantic Ocean. The future work would include the following steps:

• Consideration of the ocean circulation and its long term effect on SST and

atmospheric parameters.

• Using of realistic ocean model simulations and observations.

• Application of the EOF and CCA for both atmospheric characteristics and ocean

surface and sub-surface parameters.

103

Abbreviations

• NAO: North Atlantic Oscillation. The NAO is the dominant mode of winter

climate variability in the North Atlantic region ranging from central North

America to Europe and much into Northern Asia. The NAO is a large scale

seesaw in atmospheric mass between the subtropical high and the polar low. The

corresponding index varies from year to year, but also exhibits a tendency to

remain in one phase for intervals lasting several years. The Positive NAO index

phase shows a stronger than usual subtropical high pressure center and a deeper

than normal Icelandic low. The increased pressure difference results in more and

stronger winter storms crossing the Atlantic Ocean on a more northerly track. The

negative NAO index phase shows a weak subtropical high and a weak Icelandic

low. The reduced pressure gradient results in fewer and weaker winter storms

crossing on a more west-east pathway.

• NCEP: National Center of Environmental Prediction.

• COADS: Comprehensive Ocean-Atmospheric Dataset.

104

• EOF: Empirical Orthogonal Function. The method of empirical orthogonal

function (EOF) analysis is a decomposition of a signal or data set in terms of

orthogonal basis functions which are determined from the data.

• CCA: Canonical Correlation Analysis. A typical use for canonical correlation in

the general context is to take a two sets of variables and see what is common

amongst the two tests.

• SST: Sea Surface Temperature .

• SSP: Sea Surface Pressure .

• LSW: Labrador Sea Water .

105

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